Abstract
One way to generalize the boundary Yamabe problem posed by Escobar is to ask if a given metric on a compact manifold with boundary can be conformally deformed to have vanishing σk-curvature in the interior and constant Hk-curvature on the boundary. When restricting to the closure of the positive k-cone, this is a fully nonlinear degenerate elliptic boundary value problem with fully nonlinear Robin-type boundary condition. We prove a general bifurcation theorem which allows us to construct examples of compact Riemannian manifolds (X, g) for which this problem admits multiple non-homothetic solutions in the case when 2 k< dim X. Our examples are all such that the boundary with its induced metric is a Riemannian product of a round sphere with an Einstein manifold.
Original language | English (US) |
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Article number | 106 |
Journal | Calculus of Variations and Partial Differential Equations |
Volume | 58 |
Issue number | 3 |
DOIs | |
State | Published - Jun 1 2019 |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics