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引用次数: 0
摘要
我们研究了欧几里得空间中具有两个边界分量的旋转超曲面的斯特克洛夫特征值的尖锐上界问题，每个边界分量都与\({\mathbb {S}}^{n-1}\) 等距。对于第一个非零斯特克洛夫特征值的情况，我们给出了一个尖锐的上界\(B_n(L)\)（仅取决于维度\(n \ge 3\) 和子午线长度\(L>0\)），这个上界是通过我们明确计算的退化度量\(g^*\)达到的。我们还给出了一个仅取决于 n 的尖锐上界 \(B_n\)。我们的方法还允许我们证明这些上界的一些稳定性。
Sharp upper bounds for Steklov eigenvalues of a hypersurface of revolution with two boundary components in Euclidean space
We investigate the question of sharp upper bounds for the Steklov eigenvalues of a hypersurface of revolution in Euclidean space with two boundary components, each isometric to \({\mathbb {S}}^{n-1}\). For the case of the first non zero Steklov eigenvalue, we give a sharp upper bound \(B_n(L)\) (that depends only on the dimension \(n \ge 3\) and the meridian length \(L>0\)) which is reached by a degenerated metric \(g^*\) that we compute explicitly. We also give a sharp upper bound \(B_n\) which depends only on n. Our method also permits us to prove some stability properties of these upper bounds.
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.
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