Pub Date : 2022-06-06DOI: 10.2422/2036-2145.202112_011
Sumiya Baasandorj, Sun-Sig Byun
{"title":"Gradient estimates for Orlicz double phase problems","authors":"Sumiya Baasandorj, Sun-Sig Byun","doi":"10.2422/2036-2145.202112_011","DOIUrl":"https://doi.org/10.2422/2036-2145.202112_011","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89610121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-22DOI: 10.2422/2036-2145.202205_015
A. Alarcón, F. Lárusson
The Gauss map of a conformal minimal immersion of an open Riemann surface M into R 3 is a meromorphic function on M . In this paper, we prove that the Gauss map assignment, taking a full conformal minimal immersion M → R 3 to its Gauss map, is a Serre fibration. We then determine the homotopy type of the space of meromorphic functions on M that are the Gauss map of a complete full conformal minimal immersion, and show that it is the same as the homotopy type of the space of all continuous maps from M to the 2-sphere. We obtain analogous results for the generalised Gauss map of conformal minimal immersions M → R n for arbitrary n ≥ 3.
{"title":"The space of Gauss maps of complete minimal surfaces","authors":"A. Alarcón, F. Lárusson","doi":"10.2422/2036-2145.202205_015","DOIUrl":"https://doi.org/10.2422/2036-2145.202205_015","url":null,"abstract":"The Gauss map of a conformal minimal immersion of an open Riemann surface M into R 3 is a meromorphic function on M . In this paper, we prove that the Gauss map assignment, taking a full conformal minimal immersion M → R 3 to its Gauss map, is a Serre fibration. We then determine the homotopy type of the space of meromorphic functions on M that are the Gauss map of a complete full conformal minimal immersion, and show that it is the same as the homotopy type of the space of all continuous maps from M to the 2-sphere. We obtain analogous results for the generalised Gauss map of conformal minimal immersions M → R n for arbitrary n ≥ 3.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91359095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-20DOI: 10.2422/2036-2145.202208_024
A. Lopez, R. Muñoz, Jos'e Carlos Sierra
We give an almost complete classification of non-big Ulrich vector bundles on fourfolds. This allows to classify them in the case of Picard rank one fourfolds, of Mukai fourfolds and in the case of Del Pezzo $n$-folds for $n le 4$. We also classify Ulrich bundles with non-big determinant on Del Pezzo and Mukai $n$-folds, $n ge 2$.
给出了四折上的非大乌尔里希向量束的几乎完全分类。这允许在皮卡德排名1的情况下对它们进行四倍的分类，在Mukai排名4倍的情况下，在Del Pezzo的情况下$n$ - $n le 4$的折叠。我们还对Del Pezzo和Mukai $n$ -folds, $n ge 2$上的非大行列式Ulrich束进行了分类。
{"title":"On the classification of non-big Ulrich vector bundles on fourfolds","authors":"A. Lopez, R. Muñoz, Jos'e Carlos Sierra","doi":"10.2422/2036-2145.202208_024","DOIUrl":"https://doi.org/10.2422/2036-2145.202208_024","url":null,"abstract":"We give an almost complete classification of non-big Ulrich vector bundles on fourfolds. This allows to classify them in the case of Picard rank one fourfolds, of Mukai fourfolds and in the case of Del Pezzo $n$-folds for $n le 4$. We also classify Ulrich bundles with non-big determinant on Del Pezzo and Mukai $n$-folds, $n ge 2$.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84295976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-05DOI: 10.2422/2036-2145.202205_007
Xieping Wang
. Let X be a cohomologically ( n − 1)-complete complex manifold of dimension n ≥ 2. We prove a vanishing result for the Bott-Chern cohomology group of type (1 , 1) with compact support in X , which combined with the well-known technique of Ehrenpreis implies a Hartogs type extension theorem for pluriharmonic functions on X .
{"title":"Bott-Chern cohomology and the Hartogs extension theorem for pluriharmonic functions","authors":"Xieping Wang","doi":"10.2422/2036-2145.202205_007","DOIUrl":"https://doi.org/10.2422/2036-2145.202205_007","url":null,"abstract":". Let X be a cohomologically ( n − 1)-complete complex manifold of dimension n ≥ 2. We prove a vanishing result for the Bott-Chern cohomology group of type (1 , 1) with compact support in X , which combined with the well-known technique of Ehrenpreis implies a Hartogs type extension theorem for pluriharmonic functions on X .","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"141 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74936785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-18DOI: 10.2422/2036-2145.202210_005
Ramiro A. Lafuente, J. Stanfield
We complete the classification of compact Hermitian manifolds admitting a flat Gauduchon connection. In particular, we establish a conjecture of Yang and Zheng, showing that apart from the cases of a flat Chern or Bismut connection, such manifolds are K"ahler. More generally, we prove the same result holds when the flatness assumption is replaced by the so-called K"ahler-like condition, proving a conjecture of Angella, Otal, Ugarte and Villacampa. We also treat the non-compact case.
{"title":"Hermitian manifolds with flat Gauduchon connections","authors":"Ramiro A. Lafuente, J. Stanfield","doi":"10.2422/2036-2145.202210_005","DOIUrl":"https://doi.org/10.2422/2036-2145.202210_005","url":null,"abstract":"We complete the classification of compact Hermitian manifolds admitting a flat Gauduchon connection. In particular, we establish a conjecture of Yang and Zheng, showing that apart from the cases of a flat Chern or Bismut connection, such manifolds are K\"ahler. More generally, we prove the same result holds when the flatness assumption is replaced by the so-called K\"ahler-like condition, proving a conjecture of Angella, Otal, Ugarte and Villacampa. We also treat the non-compact case.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90780423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-14DOI: 10.2422/2036-2145.202206_007
T. Bourni, Mathew T. Langford
We prove that there exists, in every dimension, a unique (modulo rotations about the origin and time translations) convex ancient mean curvature flow in the ball with free boundary on the sphere.
我们证明了在球上有自由边界的球中存在一个唯一的(绕原点的模旋转和时间平移)凸古平均曲率流。
{"title":"Classification of convex ancient free boundary mean curvature flows in the ball","authors":"T. Bourni, Mathew T. Langford","doi":"10.2422/2036-2145.202206_007","DOIUrl":"https://doi.org/10.2422/2036-2145.202206_007","url":null,"abstract":"We prove that there exists, in every dimension, a unique (modulo rotations about the origin and time translations) convex ancient mean curvature flow in the ball with free boundary on the sphere.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"33 3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90883345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-12DOI: 10.2422/2036-2145.202208_008
Matteo Cozzi, Antonio J. Fern'andez
We consider the nonlocal Liouville type equation $$ (-Delta)^{frac{1}{2}} u = varepsilon kappa(x) e^u, quad u>0, quad mbox{in } I, qquad u = 0, quad mbox{in } mathbb{R} setminus I, $$ where $I$ is a union of $d geq 2$ disjoint bounded intervals, $kappa$ is a smooth bounded function with positive infimum and $varepsilon>0$ is a small parameter. For any integer $1 leq m leq d$, we construct a family of solutions $(u_varepsilon)_{varepsilon}$ which blow up at $m$ interior distinct points of $I$ and for which $varepsilon int_I kappa e^{u_varepsilon} , rightarrow 2 m pi$, as $varepsilon to 0$. Moreover, we show that, when $d = 2$ and $m$ is suitably large, no such construction is possible.
考虑非局部Liouville型方程$$ (-Delta)^{frac{1}{2}} u = varepsilon kappa(x) e^u, quad u>0, quad mbox{in } I, qquad u = 0, quad mbox{in } mathbb{R} setminus I, $$，其中$I$是$d geq 2$不相交有界区间的并集，$kappa$是正无穷值的光滑有界函数，$varepsilon>0$是一个小参数。对于任意整数$1 leq m leq d$，我们构造一个解族$(u_varepsilon)_{varepsilon}$，它在$I$的内部不同点$m$爆炸，对于它$varepsilon int_I kappa e^{u_varepsilon} , rightarrow 2 m pi$，为$varepsilon to 0$。此外，我们表明，当$d = 2$和$m$适当大时，不可能进行这样的构造。
{"title":"Blowing-up solutions for a nonlocal Liouville type equation","authors":"Matteo Cozzi, Antonio J. Fern'andez","doi":"10.2422/2036-2145.202208_008","DOIUrl":"https://doi.org/10.2422/2036-2145.202208_008","url":null,"abstract":"We consider the nonlocal Liouville type equation $$ (-Delta)^{frac{1}{2}} u = varepsilon kappa(x) e^u, quad u>0, quad mbox{in } I, qquad u = 0, quad mbox{in } mathbb{R} setminus I, $$ where $I$ is a union of $d geq 2$ disjoint bounded intervals, $kappa$ is a smooth bounded function with positive infimum and $varepsilon>0$ is a small parameter. For any integer $1 leq m leq d$, we construct a family of solutions $(u_varepsilon)_{varepsilon}$ which blow up at $m$ interior distinct points of $I$ and for which $varepsilon int_I kappa e^{u_varepsilon} , rightarrow 2 m pi$, as $varepsilon to 0$. Moreover, we show that, when $d = 2$ and $m$ is suitably large, no such construction is possible.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84099281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-11DOI: 10.2422/2036-2145.202105_064
H. Grunau, S. Okabe
{"title":"Willmore Obstacle Problems under Dirichlet Boundary Conditions Submitted: 2021-03-18","authors":"H. Grunau, S. Okabe","doi":"10.2422/2036-2145.202105_064","DOIUrl":"https://doi.org/10.2422/2036-2145.202105_064","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"108 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85484671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-11DOI: 10.2422/2036-2145.202105_060
P. Bousquet
{"title":"Non occurence of the Lavrentiev gap for multidimensional autonomous problems","authors":"P. Bousquet","doi":"10.2422/2036-2145.202105_060","DOIUrl":"https://doi.org/10.2422/2036-2145.202105_060","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"68 4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88479545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-06DOI: 10.2422/2036-2145.202204_005
C. Deninger
A well known argument by Serre shows that there is no Weil cohomology theory with real coefficients for smooth projective varieties over $bar{mathbb{F}}_p$. In this note we explain why no"Weil-"cohomology theory with real coefficients can exist for arithmetic schemes over spec $mathbb{Z}$, even for spectra of number rings.
{"title":"There is no Weil-cohomology theory with real coefficients for arithmetic curves","authors":"C. Deninger","doi":"10.2422/2036-2145.202204_005","DOIUrl":"https://doi.org/10.2422/2036-2145.202204_005","url":null,"abstract":"A well known argument by Serre shows that there is no Weil cohomology theory with real coefficients for smooth projective varieties over $bar{mathbb{F}}_p$. In this note we explain why no\"Weil-\"cohomology theory with real coefficients can exist for arithmetic schemes over spec $mathbb{Z}$, even for spectra of number rings.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85491930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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