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math.DG2022
A Mountain-pass Theorem in Hyperbolic Space and its Application
Junfu Yao
We develop a min-max theory for certain complete minimal hypersurfaces in hyperbolic space. In particular, we show that given two strictly stable minimal hypersurfaces that are bot…
math.DG2022
Relative Entropy of Hypersurfaces in Hyperbolic Space
Junfu Yao
We study a notion of relative entropy for certain hypersurfaces in hyperbolic space. We relate this quantity to the renormalized area introduced by Graham-Witten[RW99]. We also obt…
math.DG2020
A Uniqueness Result for Self-expanders with Small Entropy
Junfu Yao
In this short note, we prove a uniqueness result for small entropy self-expanders asymptotic to a fixed cone. This is a direct consequence of the mountain-pass theorem and the inte…