Upper bounds for higher-order Poincare constants

• Kei Funano

Bibliographic Information

Other Title

• 偏微分方程式の解の幾何的様相
• ヘンビブン ホウテイシキ ノ カイ ノ キカテキ ヨウソウ

Abstract

Here we introduce higher-order Poincaré constants for compact weighted manifolds and estimate them from above in terms of subsets. These estimates imply upper bounds for eigenvalues of the weighted Laplacian and the first nontrivial eigenvalue of the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Laplacian. In the case of the closed eigenvalue problem and the Neumann eigenvalue problem these are related to the estimates obtained by Chung-Grigor’yan-Yau and Gozlan-Herry. We also obtain similar upper bounds for Dirichlet eigenvalues and multi-way isoperimetric constants. As an application, for manifolds with boundary of nonnegative dimensional weighted Ricci curvature, we give upper bounds for inscribed radii in terms of dimension and the first Dirichlet Poincaré constant.

Journal

• 数理解析研究所講究録

  数理解析研究所講究録 (2172), 77-85, 2020-11

  [京都] : 京都大学数理解析研究所

Keywords

• Applied Mathematics
• General Mathematics

Details

• CRID: 1520009410034375296
• NII Article ID: 40022530922
• NII Book ID: AN00061013
• ISSN: 18802818
• ISSN: 10886850
• ISSN: 00029947
• DOI: 10.1090/tran/8049
• NDL BIB ID: 031373288
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I031373288
• Web Site: http://www.ams.org/tran/earlyview/#tran8049/.pdf
• Web Site: https://www.ams.org/tran/2020-373-06/S0002-9947-2020-08049-0/S0002-9947-2020-08049-0.pdf
• Text Lang: en
• NDL Source Classification:
  • ZM31(科学技術--数学)
• Data Source:
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN