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Direct Products for the Hamiltonian Density Property. 哈密顿密度性质的直接乘积。
IF 1.5 2区 数学
Journal of Geometric Analysis Pub Date : 2026-01-01 Epub Date: 2025-11-11 DOI: 10.1007/s12220-025-02246-3
Rafael B Andrist, Gaofeng Huang
{"title":"Direct Products for the Hamiltonian Density Property.","authors":"Rafael B Andrist, Gaofeng Huang","doi":"10.1007/s12220-025-02246-3","DOIUrl":"https://doi.org/10.1007/s12220-025-02246-3","url":null,"abstract":"<p><p>We show that the direct product of two Stein manifolds with the Hamiltonian density property enjoys the Hamiltonian density property as well. We investigate the relation between the Hamiltonian density property and the symplectic density property. We then establish the Hamiltonian and the symplectic density property for <math> <msup><mrow><mo>(</mo> <msup><mrow><mi>C</mi></mrow> <mo>∗</mo></msup> <mo>)</mo></mrow> <mrow><mn>2</mn> <mi>n</mi></mrow> </msup> </math> and for the so-called traceless Calogero-Moser spaces. As an application we obtain a Carleman-type approximation for Hamiltonian diffeomorphisms of a real form of the traceless Calogero-Moser space.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"36 1","pages":"8"},"PeriodicalIF":1.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12605522/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145515123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Note on a Weighted Geometric Inequality in Hyperbolic Space. 双曲空间中一个加权几何不等式的注记。
IF 1.5 2区 数学
Journal of Geometric Analysis Pub Date : 2026-01-01 Epub Date: 2026-08-12 DOI: 10.1007/s12220-026-02565-z
Botong Xu
{"title":"Note on a Weighted Geometric Inequality in Hyperbolic Space.","authors":"Botong Xu","doi":"10.1007/s12220-026-02565-z","DOIUrl":"https://doi.org/10.1007/s12220-026-02565-z","url":null,"abstract":"<p><p>In this paper, we prove that the solution to a locally constrained flow in hyperbolic space introduced by Hu et al. [14] exists for a long time and converges exponentially fast to a geodesic sphere centered at the origin if the initial hypersurface is strictly horo-convex. Unlike previous results, we do not require the initial hypersurface to be star-shaped. As a consequence, we refine an Alexandrov-Fenchel type weighted geometric inequality proved by them so that both sides are isometry-invariant.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"36 10","pages":"314"},"PeriodicalIF":1.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13469401/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148765699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two Fefferman-Type Constructions Involving Almost Grassmann Structures and Path Geometries. 涉及几乎格拉斯曼结构和路径几何的两个费弗曼型结构。
IF 1.5 2区 数学
Journal of Geometric Analysis Pub Date : 2026-01-01 Epub Date: 2026-10-13 DOI: 10.1007/s12220-026-02630-7
Zhangwen Guo
{"title":"Two Fefferman-Type Constructions Involving Almost Grassmann Structures and Path Geometries.","authors":"Zhangwen Guo","doi":"10.1007/s12220-026-02630-7","DOIUrl":"https://doi.org/10.1007/s12220-026-02630-7","url":null,"abstract":"<p><p>We introduce a Fefferman-type construction that associates an almost Grassmann structure of type <math><mrow><mo>(</mo> <mn>2</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo></mrow> </math> to every <math><mrow><mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo></mrow> </math> -dimensional path geometry. We prove that the construction is normal and provide two equivalent characterizing conditions for all almost Grassmann structures which locally arise from this construction: one in terms of certain parallel tractors and the other in terms of a Weyl connection of an almost Grassmann structure. We prove that the latter condition is independent of the choice of Weyl connection. We then introduce a related Fefferman-type construction associating an almost Grassmann structure of type <math><mrow><mo>(</mo> <mn>2</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo></mrow> </math> to every almost Grassmann structure of type (2, <i>n</i>). We prove that this construction is non-normal and characterize all almost Grassmann structures which locally arise in this way in Cartan geometric terms.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"36 12","pages":"384"},"PeriodicalIF":1.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13661732/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149197907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Lipschitz-Volume Rigidity Problem for Metric Manifolds. 度量流形的lipschitz -体积刚度问题。
IF 1.5 2区 数学
Journal of Geometric Analysis Pub Date : 2026-01-01 Epub Date: 2026-10-15 DOI: 10.1007/s12220-026-02643-2
Denis Marti
{"title":"The Lipschitz-Volume Rigidity Problem for Metric Manifolds.","authors":"Denis Marti","doi":"10.1007/s12220-026-02643-2","DOIUrl":"https://doi.org/10.1007/s12220-026-02643-2","url":null,"abstract":"<p><p>We prove a Lipschitz-volume rigidity result for 1-Lipschitz maps of non-zero degree between metric manifolds (metric spaces homeomorphic to a closed oriented manifold) and Riemannian manifolds. The proof is based on degree theory and recent developments of Lipschitz-volume rigidity for integral currents.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"36 12","pages":"388"},"PeriodicalIF":1.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13672402/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149217414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Flows of Conformally Coclosed G 2 -Structures with Dilaton. 带膨胀的共形封闭g2结构的流动。
IF 1.5 2区 数学
Journal of Geometric Analysis Pub Date : 2026-01-01 Epub Date: 2026-04-10 DOI: 10.1007/s12220-026-02416-x
Spiro Karigiannis, Sébastien Picard, Caleb Suan
{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">Flows of Conformally Coclosed <ns0:math><ns0:msub><ns0:mi>G</ns0:mi> <ns0:mn>2</ns0:mn></ns0:msub> </ns0:math> -Structures with Dilaton.","authors":"Spiro Karigiannis, Sébastien Picard, Caleb Suan","doi":"10.1007/s12220-026-02416-x","DOIUrl":"10.1007/s12220-026-02416-x","url":null,"abstract":"<p><p>We study flows of <math><msub><mi>G</mi> <mn>2</mn></msub> </math> -structures guided by the principle of dimensional reduction: natural geometric flows in <math><msub><mi>G</mi> <mn>2</mn></msub> </math> -geometry reduce to natural flows in complex geometry. Our main examples are the <math><msub><mi>G</mi> <mn>2</mn></msub> </math> -Laplacian coflow, which lifts the Kähler-Ricci flow, and a 7-dimensional lift of the anomaly flow on complex threefolds. The <math><msub><mi>G</mi> <mn>2</mn></msub> </math> -lift of the anomaly flow deforms conformally coclosed <math><msub><mi>G</mi> <mn>2</mn></msub> </math> -structures. We compare the <math><msub><mi>G</mi> <mn>2</mn></msub> </math> -anomaly flow to the <math><msub><mi>G</mi> <mn>2</mn></msub> </math> -Laplacian coflow, and investigate short-time existence and fixed points.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"36 5","pages":"171"},"PeriodicalIF":1.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13068682/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147678919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Generalised Energy Identity and Length of Necks for ε -Harmonic Maps. ε -调和映射的广义能量恒等式和颈长。
IF 1.5 2区 数学
Journal of Geometric Analysis Pub Date : 2026-01-01 Epub Date: 2026-09-22 DOI: 10.1007/s12220-026-02613-8
Andrew M Roberts
{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">The Generalised Energy Identity and Length of Necks for <ns0:math><ns0:mi>ε</ns0:mi></ns0:math> -Harmonic Maps.","authors":"Andrew M Roberts","doi":"10.1007/s12220-026-02613-8","DOIUrl":"10.1007/s12220-026-02613-8","url":null,"abstract":"<p><p>In this paper we find analogues for <math><mi>ε</mi></math> -harmonic maps to the generalised energy identity and the existence of geodesic necks result discovered by Yuxiang Li and Youde Wang for <math><mi>α</mi></math> -harmonic maps. In particular there exist specific quantities depending only on <math><mi>ε</mi></math> and the bubbling radius which entirely determine if the full energy identity holds and if a neck forms. In the case these fail we can calculate the energy lost and the length of the geodesic neck based on only these quantities and the biharmonic energy of the bubble.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"36 11","pages":"365"},"PeriodicalIF":1.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13597655/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149032186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Distributional Sectional Curvature Bounds for Riemannian Metrics of Low Regularity. 低正则性黎曼度量的分布截面曲率界。
IF 1.5 2区 数学
Journal of Geometric Analysis Pub Date : 2026-01-01 Epub Date: 2026-01-30 DOI: 10.1007/s12220-026-02339-7
Darius Erös, Michael Kunzinger, Argam Ohanyan, Alessio Vardabasso
{"title":"Distributional Sectional Curvature Bounds for Riemannian Metrics of Low Regularity.","authors":"Darius Erös, Michael Kunzinger, Argam Ohanyan, Alessio Vardabasso","doi":"10.1007/s12220-026-02339-7","DOIUrl":"10.1007/s12220-026-02339-7","url":null,"abstract":"<p><p>Sectional curvature bounds are of central importance in the study of Riemannian manifolds, both in smooth differential geometry and in the generalized synthetic setting of Alexandrov spaces. Riemannian metrics along with metric spaces of bounded sectional curvature enjoy a variety of, oftentimes rigid, geometric properties. The purpose of this article is to introduce and discuss a new notion of sectional curvature bounds for manifolds equipped with continuous Riemannian metrics of Geroch-Traschen regularity, i.e., <math> <mrow><msubsup><mi>H</mi> <mtext>loc</mtext> <mn>1</mn></msubsup> <mo>∩</mo> <msup><mi>C</mi> <mn>0</mn></msup> </mrow> </math> , based on a distributional version of the classical formula. Our main result states that for <math><mrow><mi>g</mi> <mo>∈</mo> <msup><mi>C</mi> <mn>1</mn></msup> </mrow> </math> , this new notion recovers the corresponding bound based on triangle comparison in the sense of Alexandrov. A weaker version of this statement is also proven for locally Lipschitz continuous metrics.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"36 3","pages":"92"},"PeriodicalIF":1.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12858456/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146108815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Families of proper holomorphic maps. 真全纯映射的族。
IF 1.5 2区 数学
Journal of Geometric Analysis Pub Date : 2026-01-01 Epub Date: 2026-02-02 DOI: 10.1007/s12220-026-02342-y
Barbara Drinovec Drnovšek, Jure Kališnik
{"title":"Families of proper holomorphic maps.","authors":"Barbara Drinovec Drnovšek, Jure Kališnik","doi":"10.1007/s12220-026-02342-y","DOIUrl":"10.1007/s12220-026-02342-y","url":null,"abstract":"<p><p>Given a smooth, open, oriented surface <i>X</i> endowed with a family of complex structures <math> <msub><mrow><mo>{</mo> <msub><mi>J</mi> <mi>b</mi></msub> <mo>}</mo></mrow> <mrow><mi>b</mi> <mo>∈</mo> <mi>B</mi></mrow> </msub> </math> depending continuously on the parameter <i>b</i> in a metrisable space <i>B</i>, we construct a continuous family of proper holomorphic maps <math> <mrow><msub><mi>F</mi> <mi>b</mi></msub> <mo>:</mo> <mrow><mo>(</mo> <mi>X</mi> <mo>,</mo> <msub><mi>J</mi> <mi>b</mi></msub> <mo>)</mo></mrow> <mo>→</mo> <msup><mrow><mi>C</mi></mrow> <mn>2</mn></msup> </mrow> </math> , <math><mrow><mi>b</mi> <mo>∈</mo> <mi>B</mi></mrow> </math> .</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"36 3","pages":"102"},"PeriodicalIF":1.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12864255/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146120878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Shape Optimization with Large Magnetic Fields in Two Dimensions. 二维大磁场下的形状优化。
IF 1.5 2区 数学
Journal of Geometric Analysis Pub Date : 2026-01-01 Epub Date: 2026-03-07 DOI: 10.1007/s12220-026-02363-7
Vladimir Lotoreichik, Léo Morin
{"title":"On Shape Optimization with Large Magnetic Fields in Two Dimensions.","authors":"Vladimir Lotoreichik, Léo Morin","doi":"10.1007/s12220-026-02363-7","DOIUrl":"10.1007/s12220-026-02363-7","url":null,"abstract":"<p><p>This paper aims to show that, in the limit of strong magnetic fields, the optimal domains for eigenvalues of magnetic Laplacians tend to exhibit symmetry. We establish several asymptotic bounds on magnetic eigenvalues to support this conclusion. Our main result implies that if, for a bounded simply-connected planar domain, the <i>n</i>-th eigenvalue of the magnetic Dirichlet Laplacian with uniform magnetic field is smaller than the corresponding eigenvalue for a disk of the same area, then the Fraenkel asymmetry of that domain tends to zero in the strong magnetic field limit. Comparable results are also derived for the magnetic Dirichlet Laplacian on rectangles, as well as the magnetic Dirac operator with infinite mass boundary conditions on smooth domains. As part of our analysis, we additionally provide a new estimate for the torsion function on rectangles.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"36 4","pages":"120"},"PeriodicalIF":1.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12967422/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147391448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Kähler-Einstein Metrics. Kahler-Einstein指标。
IF 1.5 2区 数学
Journal of Geometric Analysis Pub Date : 2026-01-01 Epub Date: 2026-03-19 DOI: 10.1007/s12220-026-02401-4
Friedrich Haslinger
{"title":"Kähler-Einstein Metrics.","authors":"Friedrich Haslinger","doi":"10.1007/s12220-026-02401-4","DOIUrl":"10.1007/s12220-026-02401-4","url":null,"abstract":"<p><p>We recall a simple formula for a Kähler-Einstein metric on the unit ball and on the Siegel upper half space, both together with real holomorphic vector fields and consider generalized complex ellipsoids in <math> <msup><mrow><mi>C</mi></mrow> <mi>n</mi></msup> </math> and show that the logarithm of the defining function, as a potential function, provides a pseudometric, which is Kähler-Einstein. In addition we prove that the complex ellipsoids, endowed with this pseudometric have a real holomorphic vector field, which has several far-reaching differential geometric and functional analytic consequences. Finally we give an example of a real holomorphic vector field of higher order.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"36 4","pages":"150"},"PeriodicalIF":1.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13002646/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147500613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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