Hardy and Rellich Inequalities for submanifolds in Hadamard spaces
Differential Geometry
2016-11-16 v1 Analysis of PDEs
Abstract
Some of the most known integral inequalities are the Sobolev, Hardy and Rellich inequalities in Euclidean spaces. In the context of submanifolds, the Sobolev inequality was proved by Michael-Simon and Hoffman-Spruck. Since then, a sort of applications to the submanifold theory has been derived from those inequalities. Years later, Carron obtained a Hardy inequality for submanifolds in Hadamard spaces. In this paper, we prove the general Hardy and Rellich Inequalities for submanifolds in Hadamard spaces. Some applications are given and we also analyse the equality cases.
Keywords
Cite
@article{arxiv.1611.04656,
title = {Hardy and Rellich Inequalities for submanifolds in Hadamard spaces},
author = {Marcio Batista and Heudson Mirandola and Feliciano Vitorio},
journal= {arXiv preprint arXiv:1611.04656},
year = {2016}
}