Journal of the European Mathematical Society最新文献_第3页

Cohomology of the moduli of Higgs bundles on a curve via positive characteristic 通过正特征的曲线上希格斯束模态的同调性

IF 2.6 1区数学

Journal of the European Mathematical Society Pub Date : 2023-12-16 DOI: 10.4171/jems/1393

M. A. D. de Cataldo, D. Maulik, Junliang Shen, Siqing Zhang

引用次数: 0

Rate of propagation for the Fisher-KPP equation with nonlocal diffusion and free boundaries 具有非局部扩散和自由边界的 Fisher-KPP 方程的传播速率

IF 2.6 1区数学

Journal of the European Mathematical Society Pub Date : 2023-12-16 DOI: 10.4171/jems/1392

Yihong Du, W. Ni

{"title":"Rate of propagation for the Fisher-KPP equation with nonlocal diffusion and free boundaries","authors":"Yihong Du, W. Ni","doi":"10.4171/jems/1392","DOIUrl":"https://doi.org/10.4171/jems/1392","url":null,"abstract":". In this paper, we obtain sharp estimates for the rate of propagation of the Fisher-KPP equation with nonlocal diﬀusion and free boundaries. The nonlocal diﬀusion operator is given by (cid:82) R J ( x − y ) u ( t, y ) dy − u ( t, x ), and our estimates hold for some typical classes of kernel functions J ( x ). For example, if for | x | (cid:29) 1 the kernel function satisﬁes J ( x ) ∼ | x | − γ with γ > 1, then it follows from [17] that there is a ﬁnite spreading speed when γ > 2, namely the free boundary x = h ( t ) satisﬁes lim t →∞ h ( t ) /t = c 0 for some uniquely determined positive constant c 0 depending on J , and when γ ∈ (1 , 2], lim t →∞ h ( t ) /t = ∞ ; the estimates in the current paper imply that, for t (cid:29) 1, c 0 t − h ( t ) ∼   1 when γ > 3 ln t when γ = 3 , t 3 − γ when γ ∈ (2 , 3) , and h ( t ) ∼ (cid:26) t ln t when γ = 2 , t 1 / ( γ − 1) when γ ∈ (1 , 2) . Our approach is based on subtle integral estimates and constructions of upper and lower solutions, which rely crucially on guessing correctly the order of growth of the term to be estimated. The techniques developed here lay the ground for extensions to more general situations.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138995829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Topological characteristic factors and nilsystems 拓扑特征因子与零系统

1区数学

Journal of the European Mathematical Society Pub Date : 2023-10-31 DOI: 10.4171/jems/1379

Eli Glasner, Wen Huang, Song Shao, Benjamin Weiss, Xiangdong Ye

引用次数: 7

A Tits alternative for endomorphisms of the projective line 它是投影线的自同态的替代

1区数学

Journal of the European Mathematical Society Pub Date : 2023-10-31 DOI: 10.4171/jems/1376

Jason Bell, Keping Huang, Wayne Peng, Thomas Tucker

引用次数: 0

Sharp quantitative stability of the planar Brunn–Minkowski inequality 平面Brunn-Minkowski不等式的急剧数量稳定性

1区数学

Journal of the European Mathematical Society Pub Date : 2023-10-25 DOI: 10.4171/jems/1372

Peter van Hintum, Hunter Spink, Marius Tiba

引用次数: 10

Comparison of prismatic cohomology and derived de Rham cohomology 移动上同调与派生de Rham上同调的比较

1区数学

Journal of the European Mathematical Society Pub Date : 2023-10-25 DOI: 10.4171/jems/1377

Shizhang Li, Tong Liu

引用次数: 13

Harmonic analysis on certain spherical varieties 某些球形品种的谐波分析

1区数学

Journal of the European Mathematical Society Pub Date : 2023-10-23 DOI: 10.4171/jems/1381

Jayce R. Getz, Chun-Hsien Hsu, Spencer Leslie

引用次数: 2

Bounding nonminimality and a conjecture of Borovik–Cherlin 边界非极小性与Borovik-Cherlin的一个猜想

1区数学

Journal of the European Mathematical Society Pub Date : 2023-10-11 DOI: 10.4171/jems/1384

James Freitag, Rahim Moosa

引用次数: 10

Centro-affine differential geometry and the log-Minkowski problem 中心仿射微分几何与对数-闵可夫斯基问题

1区数学

Journal of the European Mathematical Society Pub Date : 2023-10-10 DOI: 10.4171/jems/1386

Emanuel Milman

{"title":"Centro-affine differential geometry and the log-Minkowski problem","authors":"Emanuel Milman","doi":"10.4171/jems/1386","DOIUrl":"https://doi.org/10.4171/jems/1386","url":null,"abstract":"We interpret the log-Brunn–Minkowski conjecture of Böröczky–Lutwak–Yang–Zhang as a spectral problem in centro-affine differential geometry. In particular, we show that the Hilbert--Brunn--Minkowski operator coincides with the centro-affine Laplacian, thus obtaining a new avenue for tackling the conjecture using insights from affine differential geometry. As every strongly convex hypersurface in $mathbb{R}^n$ is a centro-affine unit sphere, it has constant centro-affine Ricci curvature equal to $n-2$, in stark contrast to the standard weighted Ricci curvature of the associated metric-measure space, which will in general be negative. In particular, we may use the classical argument of Lichnerowicz and a centro-affine Bochner formula to give a new proof of the Brunn–Minkowski inequality. For origin-symmetric convex bodies enjoying fairly generous curvature pinching bounds (improving with dimension), we are able to show global uniqueness in the $L^p$- and log-Minkowski problems, as well as the corresponding global $L^p$- and log-Minkowski conjectured inequalities. As a consequence, we resolve the isomorphic version of the log-Minkowski problem: for any origin-symmetric convex body $bar K$ in $mathbb{R}^n$, there exists an origin-symmetric convex body $K$ with $bar K subset K subset 8 bar K$ such that $K$ satisfies the log-Minkowski conjectured inequality, and such that $K$ is uniquely determined by its cone-volume measure $V_K$. If $bar K$ is not extremely far from a Euclidean ball to begin with, an analogous isometric result, where $8$ is replaced by $1+varepsilon$, is obtained as well.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136254446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 17

Two-well linearization for solid-solid phase transitions 固-固相变的双阱线性化

1区数学

Journal of the European Mathematical Society Pub Date : 2023-10-10 DOI: 10.4171/jems/1385

Elisa Davoli, Manuel Friedrich

{"title":"Two-well linearization for solid-solid phase transitions","authors":"Elisa Davoli, Manuel Friedrich","doi":"10.4171/jems/1385","DOIUrl":"https://doi.org/10.4171/jems/1385","url":null,"abstract":"In this paper we consider nonlinearly elastic, frame-indifferent, and singularly perturbed two-well models for materials undergoing solid-solid phase transitions in any space dimensions, and we perform a simultaneous passage to sharp-interface and small-strain limits. Sequences of deformations with equibounded energies are decomposed via suitable Caccioppoli partitions into the sum of piecewise constant rigid movements and suitably rescaled displacements. These converge to limiting partitions, deformations, and displacements, respectively. Whereas limiting deformations are simple laminates whose gradients only attain two values, the limiting displacements belong to the class of special functions with bounded variation (SBV). The latter feature elastic contributions measuring the distance to simple laminates, as well as jumps associated to two consecutive phase transitions having vanishing distance, and thus undetected by the limiting deformations. By $Gamma$- convergence we identify an effective limiting model given by the sum of a quadratic linearized elastic energy in terms of displacements along with two surface terms. The first one is proportional to the total length of interfaces created by jumps in the gradient of the limiting deformation. The second one is proportional to twice the total length of interfaces created by jumps in the limiting displacement, as well as by the boundaries of limiting partitions. A main tool of our analysis is a novel two-well rigidity estimate which has been derived in [Calc. Var. Partial Differential Equations 59, art. 44 (2020)] for a model with anisotropic second-order perturbation.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136254444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 5