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arXiv · 2004.01514

Nonuniqueness for a fully nonlinear, degenerate elliptic boundary value problem in conformal geometry

Zhengyang Shan
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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.

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Zhengyang Shan. 2020-02-26. Nonuniqueness for a fully nonlinear, degenerate elliptic boundary value problem in conformal geometry. https://arxiv.org/abs/2004.01514

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