Concentration on minimal submanifolds for a Yamabe type problem
Analysis of PDEs
2014-09-26 v1
Abstract
We construct solutions to a Yamabe type problem on a Riemannian manifold M without boundary and of dimension greater than 2, with nonlinearity close to higher critical Sobolev exponents. These solutions concentrate their mass around a non degenerate minimal submanifold of M, provided a certain geometric condition involving the sectional curvatures is satisfied. A connection with the solution of a class of P.D.E.'s on the submanifold with a singular term of attractive or repulsive type is established.
Cite
@article{arxiv.1409.7321,
title = {Concentration on minimal submanifolds for a Yamabe type problem},
author = {Shengbing Deng and Monica Musso and Angela Pistoia},
journal= {arXiv preprint arXiv:1409.7321},
year = {2014}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1107.5566