关于拉普拉斯特征函数临界集的若干注记

IF 0.4 Q3 MATHEMATICS

Annales Mathematiques du Quebec Pub Date : 2025-01-09 DOI:10.1007/s40316-024-00240-9

Chris Judge, Sugata Mondal

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引用次数: 0

摘要

我们研究了\(\Delta u = \lambda \cdot u\)解的临界点集合，特别是余维为1的临界点集合的分量。例如，我们证明，如果单连通多边形P的第二个诺伊曼特征函数有无穷多个临界点，则P是一个矩形。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Some remarks on critical sets of Laplace eigenfunctions

We study the set of critical points of a solution to \(\Delta u = \lambda \cdot u\) and in particular components of the critical set that have codimension 1. We show, for example, that if a second Neumann eigenfunction of a simply connected polygon P has infinitely many critical points, then P is a rectangle.

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来源期刊

Annales Mathematiques du Quebec MATHEMATICS-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： The goal of the Annales mathématiques du Québec (formerly: Annales des sciences mathématiques du Québec) is to be a high level journal publishing articles in all areas of pure mathematics, and sometimes in related fields such as applied mathematics, mathematical physics and computer science. Papers written in French or English may be submitted to one of the editors, and each published paper will appear with a short abstract in both languages. History: The journal was founded in 1977 as „Annales des sciences mathématiques du Québec”, in 2013 it became a Springer journal under the name of “Annales mathématiques du Québec”. From 1977 to 2018, the editors-in-chief have respectively been S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea. Les Annales mathématiques du Québec (anciennement, les Annales des sciences mathématiques du Québec) se veulent un journal de haut calibre publiant des travaux dans toutes les sphères des mathématiques pures, et parfois dans des domaines connexes tels les mathématiques appliquées, la physique mathématique et l''informatique. On peut soumettre ses articles en français ou en anglais à l''éditeur de son choix, et les articles acceptés seront publiés avec un résumé court dans les deux langues. Histoire: La revue québécoise “Annales des sciences mathématiques du Québec” était fondée en 1977 et est devenue en 2013 une revue de Springer sous le nom Annales mathématiques du Québec. De 1977 à 2018, les éditeurs en chef ont respectivement été S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea.