Sharp constants in weighted trace inequalities on Riemannian manifolds

AbstractThough there have been extensive works on best constants for Moser-Trudinger inequalities in Euclidean spaces, Heisenberg groups or compact Riemannian manifolds, much less is known for sharp constants for the Moser-Trudinger inequalities on hyperbolic spaces. Earlier works only include the sharp constant for the Moser-Trudinger inequality on the twodimensional hyperbolic disc. In this paper, we establish best constants for several types of Moser-Trudinger inequalities on high dimensional hyperbolic spaces ℍ

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SOME -HARDY AND -RELLICH TYPE INEQUALITIES WITH REMAINDER TERMS

Journal of the Australian Mathematical Society ◽

10.1017/s1446788721000100 ◽

2021 ◽

pp. 1-20

Author(s):

YONGYANG JIN ◽

SHOUFENG SHEN

Keyword(s):

Riemannian Manifolds ◽

Bounded Domains ◽

Hadamard Manifolds ◽

Sharp Constants ◽

Hyperbolic Functions

Abstract In this paper we obtain some improved $L^p$ -Hardy and $L^p$ -Rellich inequalities on bounded domains of Riemannian manifolds. For Cartan–Hadamard manifolds we prove the inequalities with sharp constants and with weights being hyperbolic functions of the Riemannian distance.

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HARDY INEQUALITIES ON RIEMANNIAN MANIFOLDS WITH NEGATIVE CURVATURE

Communications in Contemporary Mathematics ◽

10.1142/s0219199713500430 ◽

2014 ◽

Vol 16 (02) ◽

pp. 1350043 ◽

Cited By ~ 17

Author(s):

QIAOHUA YANG ◽

DAN SU ◽

YINYING KONG

Keyword(s):

Riemannian Manifold ◽

Riemannian Manifolds ◽

Negative Curvature ◽

Geodesic Distance ◽

Euclidean Spaces ◽

Sharp Constants ◽

Hardy Inequalities ◽

Simply Connected

Let M be a complete, simply connected Riemannian manifold with negative curvature. We obtain the sharp constants of Hardy and Rellich inequalities related to the geodesic distance on M. Furthermore, if M is with strictly negative curvature, we show that the LpHardy inequalities can be globally refined by adding remainder terms like the Brezis–Vázquez improvement in case p ≥ 2, which is contrary to the case of Euclidean spaces.

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Generalized sharp Hardy type and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.40.2009.604 ◽

2009 ◽

Vol 40 (4) ◽

pp. 401-413 ◽

Cited By ~ 2

Author(s):

Shihshu Walter Wei ◽

Ye Li

Keyword(s):

Fixed Point ◽

Euclidean Space ◽

Riemannian Manifolds ◽

Compact Support ◽

Hardy’S Inequality ◽

Sharp Constants ◽

Hardy Type ◽

Hardy's Inequality ◽

Nirenberg Inequality

We prove generalized Hardy's type inequalities with sharp constants and Caffarelli-Kohn-Nirenberg inequalities with sharp constants on Riemannian manifolds $M$. When the manifold is Euclidean space we recapture the sharp Caffarelli-Kohn-Nirenberg inequality. By using a double limiting argument, we obtain an inequality that implies a sharp Hardy's inequality, for functions with compact support on the manifold $M $ (that is, not necessarily on a punctured manifold $ M \backslash \{ x_0 \} $ where $x_0$ is a fixed point in $M$). Some topological and geometric applications are discussed.

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Dynamic interpolation on Riemannian manifolds: an application to interferometric imaging

Proceedings of the 2004 American Control Conference ◽

10.23919/acc.2004.1383683 ◽

2004 ◽

Cited By ~ 6

Author(s):

I.I. Hussein ◽

A.M. Bloch

Keyword(s):

Riemannian Manifolds ◽

Interferometric Imaging

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On Ricci Riemannian Manifolds

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/v10157-010-0031-7 ◽

2010 ◽

Vol 0 (-1) ◽

pp. 437-446 ◽

Cited By ~ 1

Author(s):

S. K. Saha

Keyword(s):

Riemannian Manifolds

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On the equicontinuity of families of inverse mappings of Riemannian manifolds

Ukrainian Mathematical Bulletin ◽

10.37069/1810-3200-2019-16-4-7 ◽

2019 ◽

Vol 16 (4) ◽

pp. 557-566

Author(s):

Denis Ilyutko ◽

Evgenii Sevost'yanov

Keyword(s):

Riemannian Manifolds ◽

Type Inequality ◽

The Given ◽

Range Of Values

We study homeomorphisms of Riemannian manifolds with unbounded characteristic such that the inverse mappings satisfy the Poletsky-type inequality. It is established that their families are equicontinuous if the function Q which is related to the Poletsky inequality and is responsible for a distortion of the modulus, is integrable in the given domain, here the original manifold is connected and the domain of definition and the range of values of mappings have compact closures.

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