Let T (X) be the Teichmüller space of a closed surface X of genus g ≥ 2, C(X) be the space of geodesic currents on X, and L : T (X)→ C(X) be the embedding introduced by Bonahon which maps a hyperbolic metric to its corresponding Liouville current. In this paper, we compare some quantitative relations and topological behaviors between the intersection number and the Teichmüller metric, the length spectrum metric and Thurston’s asymmetric metrics on T (X), respectively.
设T (X)为g属≥2的封闭曲面X的teichm ller空间，C(X)为X上测地线电流的空间，L: T (X)→C(X)为Bonahon引入的将双曲度规映射到相应的刘维尔电流的嵌入。本文分别比较了交点数与T (X)上的teichm ller度量、长度谱度量和Thurston不对称度量之间的定量关系和拓扑行为。
{"title":"Intersection number and some metrics on Teichmüller space","authors":"Zongliang Sun, Hui Guo","doi":"10.18910/73741","DOIUrl":"https://doi.org/10.18910/73741","url":null,"abstract":"Let T (X) be the Teichmüller space of a closed surface X of genus g ≥ 2, C(X) be the space of geodesic currents on X, and L : T (X)→ C(X) be the embedding introduced by Bonahon which maps a hyperbolic metric to its corresponding Liouville current. In this paper, we compare some quantitative relations and topological behaviors between the intersection number and the Teichmüller metric, the length spectrum metric and Thurston’s asymmetric metrics on T (X), respectively.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67914539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We will give a necessary condition for local connectedness of the space of Kleinian punctured torus group using Bromgerg’s local coordinate system and provide a sufficient condition for local connectedness on a dense subset of the necessary condition. That is, the collection of the points where the boundary of the space of punctured torus group is not locally connected is a dense subset of the points satisfying the necessary condition.
{"title":"Local connectedness of the space of punctured torus group","authors":"Sungbok Hong, Jihoon Park","doi":"10.18910/73625","DOIUrl":"https://doi.org/10.18910/73625","url":null,"abstract":"We will give a necessary condition for local connectedness of the space of Kleinian punctured torus group using Bromgerg’s local coordinate system and provide a sufficient condition for local connectedness on a dense subset of the necessary condition. That is, the collection of the points where the boundary of the space of punctured torus group is not locally connected is a dense subset of the points satisfying the necessary condition.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42492897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we prove two mutually independent theorems on the family of Fock-BargmannHartogs domains. Let D1 and D2 be two Fock-Bargmann-Hartogs domains in CN1 and CN2 , respectively. In Theorem 1, we obtain a complete description of an arbitrarily given proper holomorphic mapping between D1 and D2 in the case where N1 = N2. Also, we shall give a geometric interpretation of Theorem 1. And, in Theorem 2, we determine the structure of Aut(D1 × D2) using the data of Aut(D1) and Aut(D2) for arbitrary N1 and N2.
{"title":"TWO THEOREMS ON THE FOCK-BARGMANN-HARTOGS DOMAINS","authors":"A. Kodama, S. Shimizu","doi":"10.18910/73626","DOIUrl":"https://doi.org/10.18910/73626","url":null,"abstract":"In this paper, we prove two mutually independent theorems on the family of Fock-BargmannHartogs domains. Let D1 and D2 be two Fock-Bargmann-Hartogs domains in CN1 and CN2 , respectively. In Theorem 1, we obtain a complete description of an arbitrarily given proper holomorphic mapping between D1 and D2 in the case where N1 = N2. Also, we shall give a geometric interpretation of Theorem 1. And, in Theorem 2, we determine the structure of Aut(D1 × D2) using the data of Aut(D1) and Aut(D2) for arbitrary N1 and N2.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45809614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
$zeta(cdot)$ being the Riemann zeta function, $zeta_{sigma}(t) := frac{zeta(sigma + i t)}{zeta(sigma)}$ is, for $sigma > 1$, a characteristic function of some infinitely divisible distribution $mu_{sigma}$. A process with time parameter $sigma$ having $mu_{sigma}$ as its marginal at time $sigma$ is called a Riemann zeta process. Ehm [2] has found a functional limit theorem on this process being a backwards Levy process. In this paper, we replace $zeta(cdot)$ with a Dirichlet series $eta(cdot;a)$ generated by a nonnegative, completely multiplicative arithmetical function $a(cdot)$ satisfying (3), (4) and (5) below, and derive the same type of functional limit theorem as Ehm on the process corresponding to $eta(cdot;a)$ and being a backwards Levy process.
{"title":"A generalization of functional limit theorems on the Riemann zeta process","authors":"Satoshi Takanobu","doi":"10.18910/73631","DOIUrl":"https://doi.org/10.18910/73631","url":null,"abstract":"$zeta(cdot)$ being the Riemann zeta function, $zeta_{sigma}(t) := frac{zeta(sigma + i t)}{zeta(sigma)}$ is, for $sigma > 1$, a characteristic function of some infinitely divisible distribution $mu_{sigma}$. A process with time parameter $sigma$ having $mu_{sigma}$ as its marginal at time $sigma$ is called a Riemann zeta process. Ehm [2] has found a functional limit theorem on this process being a backwards Levy process. In this paper, we replace $zeta(cdot)$ with a Dirichlet series $eta(cdot;a)$ generated by a nonnegative, completely multiplicative arithmetical function $a(cdot)$ satisfying (3), (4) and (5) below, and derive the same type of functional limit theorem as Ehm on the process corresponding to $eta(cdot;a)$ and being a backwards Levy process.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48357315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Vector bundles, isoparametric functions and Radon transforms on symmetric spaces","authors":"Yasuyuki Nagatomo, M. Takahashi","doi":"10.18910/73623","DOIUrl":"https://doi.org/10.18910/73623","url":null,"abstract":"","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45712678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let $mathcal{G}_k$ be the gauge group of the principal $SU(4)$-bundle over $S^4$ with second Chern class $k$ and let $p$ be a prime. We show that there is a rational or $p$-local homotopy equivalence $Omegamathcal{G}_ksimeqOmegamathcal{G}_{k'}$ if and only if $(60,k)=(60,k')$.
{"title":"THE HOMOTOPY TYPES OF SU(5)-GAUGE GROUPS","authors":"Tyrone Cutler, S. Theriault","doi":"10.18910/57660","DOIUrl":"https://doi.org/10.18910/57660","url":null,"abstract":"Let $mathcal{G}_k$ be the gauge group of the principal $SU(4)$-bundle over $S^4$ with second Chern class $k$ and let $p$ be a prime. We show that there is a rational or $p$-local homotopy equivalence $Omegamathcal{G}_ksimeqOmegamathcal{G}_{k'}$ if and only if $(60,k)=(60,k')$.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48195618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We say that a curve X of genus g has maximally computed Clifford index if the Clifford index c of X is, for c > 2, computed by a linear series of the maximum possible degree d < g; then d = 2c + 3 resp. d = 2c + 4 for odd resp. even c. For odd c such curves have been studied in [6]. In this paper we analyze if/how far analoguous results hold for such curves of even Clifford index c.
{"title":"CURVES WITH MAXIMALLY COMPUTED CLIFFORD INDEX","authors":"Takaomi Kato, G. Martens","doi":"10.18910/72319","DOIUrl":"https://doi.org/10.18910/72319","url":null,"abstract":"We say that a curve X of genus g has maximally computed Clifford index if the Clifford index c of X is, for c > 2, computed by a linear series of the maximum possible degree d < g; then d = 2c + 3 resp. d = 2c + 4 for odd resp. even c. For odd c such curves have been studied in [6]. In this paper we analyze if/how far analoguous results hold for such curves of even Clifford index c.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42528100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the initial boundary value problem for a time-dependent Ginzburg-Landau model in superconductivity. First, we prove the uniform boundedness of strong solutions with respect to diffusion coefficient 0 < < 1 in the case of Coulomb gauge. Our second result is the global existence and uniqueness of the weak solutions to the limit problem when = 0.
{"title":"UNIFORM WELL-POSEDNESS FOR A TIME-DEPENDENT GINZBURG-LANDAU MODEL IN SUPERCONDUCTIVITY","authors":"Jishan Fan, B. Samet, Yong Zhou","doi":"10.18910/72318","DOIUrl":"https://doi.org/10.18910/72318","url":null,"abstract":"We study the initial boundary value problem for a time-dependent Ginzburg-Landau model in superconductivity. First, we prove the uniform boundedness of strong solutions with respect to diffusion coefficient 0 < < 1 in the case of Coulomb gauge. Our second result is the global existence and uniqueness of the weak solutions to the limit problem when = 0.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42760738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let S̃ be an analytically finite Riemann surface which is equipped with a hyperbolic metric. Let S = S̃ {one point x}. There exists a natural projection Π of the x-pointed mapping class group Modx S onto the mapping class group Mod(S̃ ). In this paper, we classify elements in the fiber Π−1(χ) for an elliptic element χ ∈ Mod(S̃ ), and give a geometric interpretation for each element in Π−1(χ). We also prove that Π−1(tn a ◦ χ) or Π−1(tn a ◦ χ−1) consists of hyperbolic mapping classes provided that tn a ◦ χ and tn a ◦ χ−1 are hyperbolic, where a is a simple closed geodesic on S̃ and ta is the positive Dehn twist along a.
设S是一个具有双曲度规的解析有限黎曼曲面。设S = S {1点x}。x点映射类组Modx S在映射类组Mod(S)上存在一个自然投影Π。本文对椭圆元χ∈Mod(S)的光纤Π−1(χ)中的元素进行了分类，并给出了Π−1(χ)中每个元素的几何解释。我们还证明Π−1(tn a◦χ)或Π−1(tn a◦χ−1)由双曲映射类组成，条件是tn a◦χ和tn a◦χ−1是双曲的，其中a是S n上的简单封闭测地线，ta是沿a的正Dehn扭转。
{"title":"A CLASSIFICATION PROBLEM ON MAPPING CLASSES ON FIBER SPACES OVER TEICHMÜLLER SPACES","authors":"Yingqing Xiao, Chao Zhang","doi":"10.18910/72314","DOIUrl":"https://doi.org/10.18910/72314","url":null,"abstract":"Let S̃ be an analytically finite Riemann surface which is equipped with a hyperbolic metric. Let S = S̃ {one point x}. There exists a natural projection Π of the x-pointed mapping class group Modx S onto the mapping class group Mod(S̃ ). In this paper, we classify elements in the fiber Π−1(χ) for an elliptic element χ ∈ Mod(S̃ ), and give a geometric interpretation for each element in Π−1(χ). We also prove that Π−1(tn a ◦ χ) or Π−1(tn a ◦ χ−1) consists of hyperbolic mapping classes provided that tn a ◦ χ and tn a ◦ χ−1 are hyperbolic, where a is a simple closed geodesic on S̃ and ta is the positive Dehn twist along a.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43854451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We establish invariants for the trace map associated to a family of 1D discrete Dirac operators with Sturmian potentials. Using these invariants we prove that the operators have purely singular continuous spectrum of zero Lebesgue measure, uniformly on the mass and parameters that define the potentials. For rotation numbers of bounded density we prove that these Dirac operators have purely α -continuous spectrum, as to the Schr¨odinger case, for some α ∈ (0 , 1). To the Sturmian Schr¨odinger and Dirac models we establish a comparison between invariants of the trace maps, which allows to compare the numbers α ’s and lower bounds on transport exponents.
{"title":"Invariants of the trace map and uniform spectral properties for discrete Sturmian Dirac operators","authors":"R. Prado, R. Charão","doi":"10.18910/72324","DOIUrl":"https://doi.org/10.18910/72324","url":null,"abstract":"We establish invariants for the trace map associated to a family of 1D discrete Dirac operators with Sturmian potentials. Using these invariants we prove that the operators have purely singular continuous spectrum of zero Lebesgue measure, uniformly on the mass and parameters that define the potentials. For rotation numbers of bounded density we prove that these Dirac operators have purely α -continuous spectrum, as to the Schr¨odinger case, for some α ∈ (0 , 1). To the Sturmian Schr¨odinger and Dirac models we establish a comparison between invariants of the trace maps, which allows to compare the numbers α ’s and lower bounds on transport exponents.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47798988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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