| Abstract: |
| I will discuss recent work with Luc Nguyen concerning a class of fully nonlinear Yamabe-type equations of negative curvature type on the upper half-space. We show that whether the hyperbolic metric is the unique solution is completely determined by a single parameter associated with the equation; in the case of non-uniqueness, we classify all other solutions. I will also discuss implications of non-uniqueness on the validity of certain estimates for the fully nonlinear Loewner-Nirenberg problem on compact manifolds with boundary. |
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