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math.DG2023
Asymptotic Plateau problem via equidistant hyperplanes
Han Hong, Haizhong Li, Meng Zhang
We show the existence of a complete, strictly locally convex hypersurface within that adheres to a curvature equation applicable to a broad range of curvature fu…
math.DG2021
Capillary surfaces: stability, index and curvature estimates
Han Hong, Artur B. Saturnino
In this paper we investigate the connection between the index and the geometry and topology of capillary surfaces. We prove an index estimate for compact capillary surfaces immerse…
math.DG2019
Index Estimates for Surfaces with Constant Mean Curvature in -dimensional Manifolds
Nicolau S. Aiex, Han Hong
We prove index estimates for closed and free boundary CMC surfaces in certain -dimensional submanifolds of some Euclidean space. When the mean curvature is large enough we are a…