Pub Date : 2011-01-01DOI: 10.2422/2036-2145.2011.2.02
V. Recupero
We prove a theorem providing a geometric characterization of BV continuous vector rate independent operators. We apply this theorem to rate independent evolution variational inequalities and deduce new continuity properties of their solution operator: the vectorial play operator
{"title":"BV solutions of rate independent variational inequalities","authors":"V. Recupero","doi":"10.2422/2036-2145.2011.2.02","DOIUrl":"https://doi.org/10.2422/2036-2145.2011.2.02","url":null,"abstract":"We prove a theorem providing a geometric characterization of BV continuous vector rate independent operators. We apply this theorem to rate independent evolution variational inequalities and deduce new continuity properties of their solution operator: the vectorial play operator","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"27 1","pages":"269-315"},"PeriodicalIF":1.4,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78037186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-01-01DOI: 10.1007/978-3-642-10988-1_4
S. Smale
{"title":"Stable Manifolds for Differential Equations and Diffeomorphisms","authors":"S. Smale","doi":"10.1007/978-3-642-10988-1_4","DOIUrl":"https://doi.org/10.1007/978-3-642-10988-1_4","url":null,"abstract":"","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"19 2 1","pages":"93-126"},"PeriodicalIF":1.4,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83282921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-01-01DOI: 10.2422/2036-2145.2011.2.03
James A. McCoy
We consider closed hypersurfaces which shrink self-similarly under a natural class of fully nonlinear curvature flows. For those flows in our class with speeds homogeneous of degree 1 and either convex or concave, we show that the only such hypersurfaces are shrinking spheres. In the setting of convex hypersurfaces, we show under a weaker second derivative condition on the speed that again only shrinking spheres are possible. For surfaces this result is extended in some cases by a different method to speeds of homogeneity greater than 1. Finally we show that self-similar hypersurfaces with sufficiently pinched principal curvatures, depending on the flow speed, are again necessarily spheres.
{"title":"Self-similar solutions of fully nonlinear curvature flows","authors":"James A. McCoy","doi":"10.2422/2036-2145.2011.2.03","DOIUrl":"https://doi.org/10.2422/2036-2145.2011.2.03","url":null,"abstract":"We consider closed hypersurfaces which shrink self-similarly under a natural class of fully nonlinear curvature flows. For those flows in our class with speeds homogeneous of degree 1 and either convex or concave, we show that the only such hypersurfaces are shrinking spheres. In the setting of convex hypersurfaces, we show under a weaker second derivative condition on the speed that again only shrinking spheres are possible. For surfaces this result is extended in some cases by a different method to speeds of homogeneity greater than 1. Finally we show that self-similar hypersurfaces with sufficiently pinched principal curvatures, depending on the flow speed, are again necessarily spheres.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"4 1","pages":"317-333"},"PeriodicalIF":1.4,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87326681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-12-24DOI: 10.2422/2036-2145.201103_007
L. Brandolini, C. Choirat, L. Colzani, G. Gigante, Raffaello Seri, G. Travaglini
We study the error in quadrature rules on a compact manifold. Our estimates are in the same spirit of the Koksma-Hlawka inequality and they depend on a sort of discrepancy of the sampling points and a generalized variation of the function. In particular, we give sharp quantitative estimates for quadrature rules of functions in Sobolev classes.
{"title":"Quadrature rules and distribution of points on manifolds","authors":"L. Brandolini, C. Choirat, L. Colzani, G. Gigante, Raffaello Seri, G. Travaglini","doi":"10.2422/2036-2145.201103_007","DOIUrl":"https://doi.org/10.2422/2036-2145.201103_007","url":null,"abstract":"We study the error in quadrature rules on a compact manifold. Our estimates are in the same spirit of the Koksma-Hlawka inequality and they depend on a sort of discrepancy of the sampling points and a generalized variation of the function. In particular, we give sharp quantitative estimates for quadrature rules of functions in Sobolev classes.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"58 1","pages":"889-923"},"PeriodicalIF":1.4,"publicationDate":"2010-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80327993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-03-15DOI: 10.2422/2036-2145.2011.4.01
S. Pigola, M. Rigoli, Michele Rimoldi, A. G. Setti
We introduce a natural extension of the concept of gradient Ricci soliton: the Ricci almost soliton. We provide existence and rigidity results, we deduce a-priori curvature estimates and isolation phenomena, and we investigate some topological properties. A number of differential identities involving the relevant geometric quantities are derived. Some basic tools from the weighted manifold theory such as general weighted volume comparisons and maximum principles at infinity for diffusion operators are discussed.
{"title":"Ricci almost solitons","authors":"S. Pigola, M. Rigoli, Michele Rimoldi, A. G. Setti","doi":"10.2422/2036-2145.2011.4.01","DOIUrl":"https://doi.org/10.2422/2036-2145.2011.4.01","url":null,"abstract":"We introduce a natural extension of the concept of gradient Ricci soliton: the Ricci almost soliton. We provide existence and rigidity results, we deduce a-priori curvature estimates and isolation phenomena, and we investigate some topological properties. A number of differential identities involving the relevant geometric quantities are derived. Some basic tools from the weighted manifold theory such as general weighted volume comparisons and maximum principles at infinity for diffusion operators are discussed.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"51 1","pages":"757-799"},"PeriodicalIF":1.4,"publicationDate":"2010-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74602052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-01-01DOI: 10.2422/2036-2145.2010.3.05
R. Alessandroni, C. Sinestrari
We study the evolution of a closed hypersurface of the euclidean space by a flow whose speed is given by a power of the scalar curvature. We prove that, if the initial shape is convex and satisfies a suitable pinching condition, the solution shrinks to a point in finite time and converges to a sphere after rescaling. We also give an example of a nonconvex hypersurface which develops a neckpinch singularity.
{"title":"Evolution of hypersurfaces by powers of the scalar curvature","authors":"R. Alessandroni, C. Sinestrari","doi":"10.2422/2036-2145.2010.3.05","DOIUrl":"https://doi.org/10.2422/2036-2145.2010.3.05","url":null,"abstract":"We study the evolution of a closed hypersurface of the euclidean space by a flow whose speed is given by a power of the scalar curvature. We prove that, if the initial shape is convex and satisfies a suitable pinching condition, the solution shrinks to a point in finite time and converges to a sphere after rescaling. We also give an example of a nonconvex hypersurface which develops a neckpinch singularity.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"24 1","pages":"541-571"},"PeriodicalIF":1.4,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78841972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-12-04DOI: 10.2422/2036-2145.2005.4.05
R. Léandre
{"title":"Stochastic Poisson-Sigma model","authors":"R. Léandre","doi":"10.2422/2036-2145.2005.4.05","DOIUrl":"https://doi.org/10.2422/2036-2145.2005.4.05","url":null,"abstract":"","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"88 1","pages":"653-667"},"PeriodicalIF":1.4,"publicationDate":"2009-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91037981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-12-02DOI: 10.2422/2036-2145.2007.4.01
M. Peletier, R. Planqué, Matthias Röger
OGER Abstract. We derive a new criterion for a real-valued function u to be in the Sobolev space W 1,2 (R n ). This criterion consists of comparing the value of a functional ! f (u) with the values of the same functional applied to convolutions of u with a Dirac sequence. The difference of these values converges to zero as the convolutions approach u, and we prove that the rate of convergence to zero is connected to regularity: u ! W 1,2 if and only if the convergence is sufficiently fast. We finally apply our criterium to a minimization problem with constraints, where regularity of minimizers cannot be deduced from the Euler-Lagrange equa- tion.
{"title":"Sobolev regularity via the convergence rate of convolutions and Jensen's inequality","authors":"M. Peletier, R. Planqué, Matthias Röger","doi":"10.2422/2036-2145.2007.4.01","DOIUrl":"https://doi.org/10.2422/2036-2145.2007.4.01","url":null,"abstract":"OGER Abstract. We derive a new criterion for a real-valued function u to be in the Sobolev space W 1,2 (R n ). This criterion consists of comparing the value of a functional ! f (u) with the values of the same functional applied to convolutions of u with a Dirac sequence. The difference of these values converges to zero as the convolutions approach u, and we prove that the rate of convergence to zero is connected to regularity: u ! W 1,2 if and only if the convergence is sufficiently fast. We finally apply our criterium to a minimization problem with constraints, where regularity of minimizers cannot be deduced from the Euler-Lagrange equa- tion.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"17 6 1","pages":"499-510"},"PeriodicalIF":1.4,"publicationDate":"2009-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83445055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-11-02DOI: 10.2422/2036-2145.201003_006
V. Minerbe, Daniel Maerten
We prove a positive-mass theorem for complete K¨ ahler manifolds that are asymptotic to the complex hyperbolic space.
我们证明了复双曲空间渐近的完全K¨ahler流形的一个正质量定理。
{"title":"A mass for asymptotically complex hyperbolic manifolds","authors":"V. Minerbe, Daniel Maerten","doi":"10.2422/2036-2145.201003_006","DOIUrl":"https://doi.org/10.2422/2036-2145.201003_006","url":null,"abstract":"We prove a positive-mass theorem for complete K¨ ahler manifolds that are asymptotic to the complex hyperbolic space.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"140 1","pages":"875-902"},"PeriodicalIF":1.4,"publicationDate":"2009-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88735670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-06-18DOI: 10.2422/2036-2145.2009.2.06
S. Borghesi
In the paper [2] we constructed (co)homology theories on the category of smooth schemes which share some of the some of the defining properties of the (co)homology theories induced by the Morava k-theory spactra in classical homotopy theory. Some proofs used the topological realization functor (cf. [8]). The existence of that functor requires the base field k to be embedded in C. In this manuscript we investigate up to what extent we can obtain the same results under the sole assumption of perfectness of the base field. The results proved here guarantee the existence of spectra i satisfying the same properties as in [2], provided that the algebra of all the bistable motivic cohomology operations verifies an assumption involving the Milnor operation Qt . Mathematics Subject Classification (2000): 14F42 (primary); 55P42, 14A15 (secondary).
{"title":"Algebraic Morava K-theory spectra over perfect fields","authors":"S. Borghesi","doi":"10.2422/2036-2145.2009.2.06","DOIUrl":"https://doi.org/10.2422/2036-2145.2009.2.06","url":null,"abstract":"In the paper [2] we constructed (co)homology theories on the category of smooth schemes which share some of the some of the defining properties of the (co)homology theories induced by the Morava k-theory spactra in classical homotopy theory. Some proofs used the topological realization functor (cf. [8]). The existence of that functor requires the base field k to be embedded in C. In this manuscript we investigate up to what extent we can obtain the same results under the sole assumption of perfectness of the base field. The results proved here guarantee the existence of spectra i satisfying the same properties as in [2], provided that the algebra of all the bistable motivic cohomology operations verifies an assumption involving the Milnor operation Qt . Mathematics Subject Classification (2000): 14F42 (primary); 55P42, 14A15 (secondary).","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"37 1","pages":"369-390"},"PeriodicalIF":1.4,"publicationDate":"2009-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80617844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：