Quantitative Rellich inequalities on Finsler - Hadamard manifolds

Alexandru Kristály, Dušan Repovš

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In this paper, we are dealing with quantitative Rellich inequalities on Finsler-Hadamard manifolds where the remainder terms are expressed by means of the flag curvature. By exploring various arguments from Finsler geometry and PDEs on manifolds, we show that more weighty curvature implies more powerful improvements in Rellich inequalities. The sharpness of the involved constants is also studied. Our results complement those of Yang, Su and Kong [Hardy inequalities on Riemannian manifolds with negative curvature, Commun. Contemp. Math. 16 (2014), Article ID: 1350043, 24 pp.].

Original languageEnglish
Article number1650020
JournalCommunications in Contemporary Mathematics
Volume18
Issue number6
DOIs
Publication statusPublished - Dec 1 2016

Keywords

  • Finsler-Hadamard manifold
  • Finsler-Laplace operator
  • Rellich inequality
  • curvature

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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