Nonuniqueness for a fully nonlinear, degenerate elliptic boundary value problem in conformal geometry
Differential Geometry
2020-04-06 v1
Abstract
We study the problem of conformally deforming a manifold with boundary to have vanishing {\sigma}4-curvature in the interior and constant H4- curvature on the boundary. We prove that there are geometrically distinct solutions using bifurcation results proven by Case, Moreira and Wang. Surprisingly, our construction via products of a sphere and hyperbolic space only works for a finite set of dimensions.
Cite
@article{arxiv.2004.01514,
title = {Nonuniqueness for a fully nonlinear, degenerate elliptic boundary value problem in conformal geometry},
author = {Zhengyang Shan},
journal= {arXiv preprint arXiv:2004.01514},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1809.00104 by other authors