Journal of Geometric Analysis最新文献_第2页

On the Gradient of the Torsion Function for Elongated Cylinders. 关于细长圆柱体扭转函数的梯度。

IF 1.5 2区数学

Journal of Geometric Analysis Pub Date : 2026-01-01 Epub Date: 2026-07-25 DOI: 10.1007/s12220-026-02554-2

M van den Berg

{"title":"On the Gradient of the Torsion Function for Elongated Cylinders.","authors":"M van den Berg","doi":"10.1007/s12220-026-02554-2","DOIUrl":"https://doi.org/10.1007/s12220-026-02554-2","url":null,"abstract":"Let <math> <mrow><mrow><mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>L</mi> <mo>)</mo></mrow> <mo>×</mo> <msub><mi>E</mi> <mi>a</mi></msub> <mo>⊂</mo> <msup><mrow><mi>R</mi></mrow> <mrow><mi>d</mi> <mo>+</mo> <mn>1</mn></mrow> </msup> </mrow> </math> denote the cylinder of length L, and base <math> <mrow><msub><mi>E</mi> <mi>a</mi></msub> <mo>⊂</mo> <msup><mrow><mi>R</mi></mrow> <mi>d</mi></msup> <mo>,</mo></mrow> </math> where <math><msub><mi>E</mi> <mi>a</mi></msub> </math> is an open ellipsoid with semi-axes <math><mrow><mi>a</mi> <mo>=</mo> <mo>(</mo> <msub><mi>a</mi> <mn>1</mn></msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub><mi>a</mi> <mi>d</mi></msub> <mo>)</mo></mrow> </math> . Let <math><msub><mi>w</mi> <mrow><mrow><mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>L</mi> <mo>)</mo></mrow> <mo>×</mo> <msub><mi>E</mi> <mi>a</mi></msub> </mrow> </msub> </math> denote its torsion function. Heat equation tools are used to show that (i) if <math><msub><mi>E</mi> <mi>a</mi></msub> </math> has small eccentricity and L is sufficiently large, then the maxima of <math> <mrow><mrow><mo>|</mo> <mi>∇</mi></mrow> <msub><mi>w</mi> <mrow><mrow><mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>L</mi> <mo>)</mo></mrow> <mo>×</mo> <msub><mi>E</mi> <mi>a</mi></msub> </mrow> </msub> <mrow><mo>|</mo></mrow> </mrow> </math> are located at the centres (0, 0) and (L, 0) respectively, (ii) if <math><msub><mi>E</mi> <mi>a</mi></msub> </math> has large eccentricity and L is sufficiently large, then the maxima are located on the lateral side of the cylinder.","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"36 9","pages":"298"},"PeriodicalIF":1.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13401543/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148594766","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

A General Nonuniqueness Result for Yamabe-Type Problems for Conformally Variational Riemannian Invariants. 共形变分黎曼不变量的yamabe型问题的一般非唯一性结果。

IF 1.5 2区数学

Journal of Geometric Analysis Pub Date : 2026-01-01 Epub Date: 2026-09-11 DOI: 10.1007/s12220-026-02598-4

João H Andrade, Jeffrey S Case, Paolo Piccione, Juncheng Wei

引用次数: 0

On the Lavrentiev Gap for Manifold-Valued Maps. 流形值映射的Lavrentiev缺口。

IF 1.5 2区数学

Journal of Geometric Analysis Pub Date : 2026-01-01 Epub Date: 2026-10-07 DOI: 10.1007/s12220-026-02628-1

Carlo Alberto Antonini, Filomena De Filippis, Cintia Pacchiano Camacho

引用次数: 0

Free Boundary Hamiltonian Stationary Lagrangian Discs in C 2. c2中的自由边界哈密顿静止拉格朗日盘。

IF 1.2 2区数学

Journal of Geometric Analysis Pub Date : 2025-01-01 Epub Date: 2025-04-04 DOI: 10.1007/s12220-025-01962-0

Filippo Gaia

{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">Free Boundary Hamiltonian Stationary Lagrangian Discs in <ns0:math> <ns0:msup><ns0:mrow><ns0:mi>C</ns0:mi></ns0:mrow> <ns0:mn>2</ns0:mn></ns0:msup></ns0:math>.","authors":"Filippo Gaia","doi":"10.1007/s12220-025-01962-0","DOIUrl":"https://doi.org/10.1007/s12220-025-01962-0","url":null,"abstract":"Let <math><mrow><mi>Ω</mi> <mo>⊂</mo> <msup><mrow><mi>C</mi></mrow> <mn>2</mn></msup> </mrow> </math> be a smooth domain. We establish conditions under which a weakly conformal, branched <math><mi>Ω</mi></math> -free boundary Hamiltonian stationary Lagrangian immersion u of a disc in <math> <msup><mrow><mi>C</mi></mrow> <mn>2</mn></msup> </math> is a <math><mi>Ω</mi></math> -free boundary minimal immersion. We deduce that if <math><mi>u</mi></math> is a weakly conformal, branched <math> <mrow><msub><mi>B</mi> <mn>1</mn></msub> <mrow><mo>(</mo> <mn>0</mn> <mo>)</mo></mrow> </mrow> </math> -free boundary Hamiltonian stationary Lagrangian immersion of a disc with Legendrian boundary, then <math><mrow><mi>u</mi> <mo>(</mo> <msup><mi>D</mi> <mn>2</mn></msup> <mo>)</mo></mrow> </math> is a Lagrangian equatorial plane disc. Furthermore, we present examples of <math><mi>Ω</mi></math> -free boundary Hamiltonian stationary discs, demonstrating the optimality of our assumptions.","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"35 5","pages":"160"},"PeriodicalIF":1.2,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11971164/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143797164","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

Geometric Bounds for Low Steklov Eigenvalues of Finite Volume Hyperbolic Surfaces. 有限体积双曲曲面的低Steklov特征值的几何界。

IF 1.2 2区数学

Journal of Geometric Analysis Pub Date : 2025-01-01 Epub Date: 2025-04-04 DOI: 10.1007/s12220-025-01990-w

Asma Hassannezhad, Antoine Métras, Hélène Perrin

引用次数: 0

On the Cheeger Inequality in Carnot-Carathéodory Spaces. carnot - carathacimodory空间中的Cheeger不等式。

IF 1.2 2区数学

Journal of Geometric Analysis Pub Date : 2025-01-01 Epub Date: 2025-02-06 DOI: 10.1007/s12220-025-01912-w

Martijn Kluitenberg

引用次数: 0

Lipschitz Stability of Travel Time Data. 旅行时间数据的Lipschitz稳定性。

IF 1.2 2区数学

Journal of Geometric Analysis Pub Date : 2025-01-01 Epub Date: 2025-06-28 DOI: 10.1007/s12220-025-02084-3

Joonas Ilmavirta, Antti Kykkänen, Matti Lassas, Teemu Saksala, Andrew Shedlock

引用次数: 0

On the Isoperimetric and Isodiametric Inequalities and the Minimisation of Eigenvalues of the Laplacian. 等周等径不等式及拉普拉斯函数特征值的最小化。

IF 1.2 2区数学

Journal of Geometric Analysis Pub Date : 2025-01-01 Epub Date: 2025-01-04 DOI: 10.1007/s12220-024-01887-0

Sam Farrington

引用次数: 0

Symbolic Calculus for a Class of Pseudodifferential Operators with Applications to Compactness. 一类伪微分算子的符号演算及其在紧性上的应用。

IF 1.5 2区数学

Journal of Geometric Analysis Pub Date : 2025-01-01 Epub Date: 2025-08-05 DOI: 10.1007/s12220-025-02128-8

Árpád Bényi, Tadahiro Oh, Rodolfo H Torres

引用次数: 0

Interpolating with generalized Assouad dimensions. 广义关联维插值。

IF 1.2 2区数学

Journal of Geometric Analysis Pub Date : 2025-01-01 Epub Date: 2025-07-12 DOI: 10.1007/s12220-025-02099-w

Amlan Banaji, Alex Rutar, Sascha Troscheit

{"title":"Interpolating with generalized Assouad dimensions.","authors":"Amlan Banaji, Alex Rutar, Sascha Troscheit","doi":"10.1007/s12220-025-02099-w","DOIUrl":"10.1007/s12220-025-02099-w","url":null,"abstract":"The <math><mi>ϕ</mi></math> -Assouad dimensions are a family of dimensions which interpolate between the upper box and Assouad dimensions. They are a generalization of the well-studied Assouad spectrum with a more general form of scale sensitivity that is often closely related to \"phase-transition\" phenomena in sets. In this article we establish a number of key properties of the <math><mi>ϕ</mi></math> -Assouad dimensions which help to clarify their behaviour. We prove for any bounded doubling metric space F and <math><mrow><mi>α</mi> <mo>∈</mo> <mi>R</mi></mrow> </math> satisfying <math> <mrow> <msub><mover><mtext>dim</mtext> <mo>¯</mo></mover> <mtext>B</mtext></msub> <mi>F</mi> <mo><</mo> <mi>α</mi> <mo>≤</mo> <msub><mtext>dim</mtext> <mtext>A</mtext></msub> <mi>F</mi></mrow> </math> that there is a function <math><mi>ϕ</mi></math> so that the <math><mi>ϕ</mi></math> -Assouad dimension of F is equal to <math><mi>α</mi></math> . We further show that the \"upper\" variant of the dimension is fully determined by the <math><mi>ϕ</mi></math> -Assouad dimension, and that homogeneous Moran sets are in a certain sense generic for these dimensions. Further, we study explicit examples of sets where the Assouad spectrum does not reach the Assouad dimension. We prove a precise formula for the <math><mi>ϕ</mi></math> -Assouad dimensions for the boundary of Galton-Watson trees that correspond to a general class of stochastically self-similar sets, including Mandelbrot percolation. The proof of this result combines a sharp large deviations theorem for Galton-Watson processes with bounded offspring distribution and a general Borel-Cantelli-type lemma for infinite structures in random trees. Finally, we obtain results on the <math><mi>ϕ</mi></math> -Assouad dimensions of overlapping self-similar sets and decreasing sequences with decreasing gaps.","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"35 9","pages":"270"},"PeriodicalIF":1.2,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12255623/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144638777","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