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Communications in Contemporary Mathematics最新文献

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Persistent homology for functionals 函数的持久同源性
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2023-12-30 DOI: 10.1142/s0219199723500554
Ulrich Bauer, Anibal M. Medina-Mardones, Maximilian Schmahl
{"title":"Persistent homology for functionals","authors":"Ulrich Bauer, Anibal M. Medina-Mardones, Maximilian Schmahl","doi":"10.1142/s0219199723500554","DOIUrl":"https://doi.org/10.1142/s0219199723500554","url":null,"abstract":"<p>We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence diagrams, which, in particular, implies that they satisfy generalized Morse inequalities. We illustrate the applicability of these results by recasting the original proof of the Unstable Minimal Surface Theorem given by Morse and Tompkins in a modern and rigorous framework.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072618","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}
引用次数: 0
Fractional anisotropic Calderón problem on complete Riemannian manifolds 完整黎曼流形上的分数各向异性卡尔德龙问题
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2023-12-09 DOI: 10.1142/s0219199723500578
Mourad Choulli, El Maati Ouhabaz
{"title":"Fractional anisotropic Calderón problem on complete Riemannian manifolds","authors":"Mourad Choulli, El Maati Ouhabaz","doi":"10.1142/s0219199723500578","DOIUrl":"https://doi.org/10.1142/s0219199723500578","url":null,"abstract":"<p>We prove that the metric tensor <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>g</mi></math></span><span></span> of a complete Riemannian manifold is uniquely determined, up to isometry, from the knowledge of a local source-to-solution operator associated with a fractional power of the Laplace–Beltrami operator <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi mathvariant=\"normal\">Δ</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span><span></span>. Our result holds under the condition that the metric tensor <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>g</mi></math></span><span></span> is known in an arbitrary small subdomain. We also consider the case of closed manifolds and provide an improvement of the main result in [A. Feizmohammadi, T. Ghosh, K. Krupchyk and G. Uhlmann, Fractional anisotropic Calderón problem on closed Riemannian manifolds, preprint (2021); arXiv:2112.03480].</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072490","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}
引用次数: 0
Harmonic maps on locally conformal almost cosymplectic manifolds 局部保角近折射流形上的谐波映射
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2023-11-17 DOI: 10.1142/s0219199723500529
C. Gherghe, G. Vîlcu
{"title":"Harmonic maps on locally conformal almost cosymplectic manifolds","authors":"C. Gherghe, G. Vîlcu","doi":"10.1142/s0219199723500529","DOIUrl":"https://doi.org/10.1142/s0219199723500529","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139263090","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}
引用次数: 0
On exponential stability of switched functional differential equations with average dwell-time 论具有平均停留时间的开关函数微分方程的指数稳定性
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2023-11-17 DOI: 10.1142/s021919972350058x
P. H. A. Ngoc, Le Trung Hieu, Thai Bao Tran
{"title":"On exponential stability of switched functional differential equations with average dwell-time","authors":"P. H. A. Ngoc, Le Trung Hieu, Thai Bao Tran","doi":"10.1142/s021919972350058x","DOIUrl":"https://doi.org/10.1142/s021919972350058x","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139265298","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}
引用次数: 0
Convexity of energy functions of harmonic maps homotopic to covering maps of surfaces 与曲面覆盖图同源的谐波图能量函数的凸性
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2023-11-17 DOI: 10.1142/s0219199723500542
Inkang Kim, Xueyuan Wan, Genkai Zhang
{"title":"Convexity of energy functions of harmonic maps homotopic to covering maps of surfaces","authors":"Inkang Kim, Xueyuan Wan, Genkai Zhang","doi":"10.1142/s0219199723500542","DOIUrl":"https://doi.org/10.1142/s0219199723500542","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139263453","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}
引用次数: 0
Boundary restricted Brunn-Minkowski inequalities 边界限制的布伦-闵科夫斯基不等式
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2023-11-17 DOI: 10.1142/s0219199723500566
S. Artstein-Avidan, Tomer Falah, Boaz A. Slomka
{"title":"Boundary restricted Brunn-Minkowski inequalities","authors":"S. Artstein-Avidan, Tomer Falah, Boaz A. Slomka","doi":"10.1142/s0219199723500566","DOIUrl":"https://doi.org/10.1142/s0219199723500566","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139263921","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}
引用次数: 0
Fast reaction limit of reaction diffusion systems with nonlinear diffusion 非线性扩散反应扩散系统的快速反应极限
2区 数学
Communications in Contemporary Mathematics Pub Date : 2023-11-10 DOI: 10.1142/s0219199723500426
Elaine Crooks, Yini Du
{"title":"Fast reaction limit of reaction diffusion systems with nonlinear diffusion","authors":"Elaine Crooks, Yini Du","doi":"10.1142/s0219199723500426","DOIUrl":"https://doi.org/10.1142/s0219199723500426","url":null,"abstract":"In this paper, we present an approach to characterizing fast-reaction limits of systems with nonlinear diffusion, when there are either two reaction–diffusion equations, or one reaction–diffusion equation and one ordinary differential equation, on unbounded domains. Here, we replace the terms of the form [Formula: see text] in usual reaction–diffusion equation, which represent linear diffusion, by terms of form [Formula: see text], representing nonlinear diffusion. We prove the convergence in the fast-reaction limit [Formula: see text] that is determined by the unique solution of a certain scalar nonlinear diffusion problem.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135088359","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}
引用次数: 1
Properties of gradient maps associated with action of real reductive group 与实约化群作用相关的梯度映射的性质
2区 数学
Communications in Contemporary Mathematics Pub Date : 2023-11-08 DOI: 10.1142/s0219199723500517
Leonardo Biliotti, Joshua O. Windare
{"title":"Properties of gradient maps associated with action of real reductive group","authors":"Leonardo Biliotti, Joshua O. Windare","doi":"10.1142/s0219199723500517","DOIUrl":"https://doi.org/10.1142/s0219199723500517","url":null,"abstract":"Let [Formula: see text] be a Kähler manifold and let [Formula: see text] be a compact connected Lie group with Lie algebra [Formula: see text] acting on [Formula: see text] and preserving [Formula: see text]. We assume that the [Formula: see text]-action extends holomorphically to an action of the complexified group [Formula: see text] and the [Formula: see text]-action on [Formula: see text] is Hamiltonian. Then there exists a [Formula: see text]-equivariant momentum map [Formula: see text]. If [Formula: see text] is a closed subgroup such that the Cartan decomposition [Formula: see text] induces a Cartan decomposition [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] is the Lie algebra of [Formula: see text], there is a corresponding gradient map [Formula: see text]. If [Formula: see text] is a [Formula: see text]-invariant compact and connected real submanifold of [Formula: see text] we may consider [Formula: see text] as a mapping [Formula: see text] Given an [Formula: see text]-invariant scalar product on [Formula: see text], we obtain a Morse like function [Formula: see text] on [Formula: see text]. We point out that, without the assumption that [Formula: see text] is a real analytic manifold, the Lojasiewicz gradient inequality holds for [Formula: see text]. Therefore, the limit of the negative gradient flow of [Formula: see text] exists and it is unique. Moreover, we prove that any [Formula: see text]-orbit collapses to a single [Formula: see text]-orbit and two critical points of [Formula: see text] which are in the same [Formula: see text]-orbit belong to the same [Formula: see text]-orbit. We also investigate convexity properties of the gradient map [Formula: see text] in the Abelian case. In particular, we study two-orbit variety [Formula: see text] and we investigate topological and cohomological properties of [Formula: see text].","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292689","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}
引用次数: 2
The bernstein problem for (X, Y)-lipschitz surfaces in three-dimensional sub-finsler heisenberg groups 三维亚finsler - heisenberg群中(X, Y)-lipschitz曲面的bernstein问题
2区 数学
Communications in Contemporary Mathematics Pub Date : 2023-10-13 DOI: 10.1142/s0219199723500487
Gianmarco Giovannardi, Manuel Ritore
{"title":"The bernstein problem for (<i>X</i>, <i>Y</i>)-lipschitz surfaces in three-dimensional sub-finsler heisenberg groups","authors":"Gianmarco Giovannardi, Manuel Ritore","doi":"10.1142/s0219199723500487","DOIUrl":"https://doi.org/10.1142/s0219199723500487","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135853587","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}
引用次数: 0
Timelike Ricci bounds for low regularity spacetimes by optimal transport 低正则时空最优输运的类时Ricci界
2区 数学
Communications in Contemporary Mathematics Pub Date : 2023-10-13 DOI: 10.1142/s0219199723500499
Mathias Braun, Matteo Calisti
{"title":"Timelike Ricci bounds for low regularity spacetimes by optimal transport","authors":"Mathias Braun, Matteo Calisti","doi":"10.1142/s0219199723500499","DOIUrl":"https://doi.org/10.1142/s0219199723500499","url":null,"abstract":"We prove that a globally hyperbolic smooth spacetime endowed with a $smash{mathrm{C}^1}$-Lorentzian metric whose Ricci tensor is bounded from below in all timelike directions, in a distributional sense, obeys the timelike measure-contraction property. This result includes a class of spacetimes with borderline regularity for which local existence results for the vacuum Einstein equation are known in the setting of spaces with timelike Ricci bounds in a synthetic sense. In particular, these spacetimes satisfy timelike Brunn-Minkowski, Bonnet-Myers, and Bishop-Gromov inequalities in sharp form, without any timelike nonbranching assumption. If the metric is even $smash{mathrm{C}^{1,1}}$, in fact the stronger timelike curvature-dimension condition holds. In this regularity, we also obtain uniqueness of chronological optimal couplings and chronological geodesics.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135853269","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}
引用次数: 1
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