Quantitative Rellich inequalities on Finsler-Hadamard manifolds (Q2828659)
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scientific article; zbMATH DE number 6643612
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quantitative Rellich inequalities on Finsler-Hadamard manifolds |
scientific article; zbMATH DE number 6643612 |
Statements
26 October 2016
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Rellich inequality
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Finsler-Hadamard manifold
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Finsler-Laplace operator
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curvature
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Quantitative Rellich inequalities on Finsler-Hadamard manifolds (English)
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In the paper under review, the authors deal 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, the authors show that more weighty curvature implies more powerful improvements in Rellich inequalities. The sharpness of the involved constants is also studied. The main results obtained in the paper (Theorems 3.1 and 3.2) complement those of \textit{Q. Yang} et al. [Commun. Contemp. Math. 16, No. 2, Article ID 1350043, 24 p. (2014; Zbl 1294.26019)].
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