Chao Xia

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math.DG2025

Stable $(r + 1)$ -th capillary hypersurfaces

Jinyu Guo, Haizhong Li, Chao Xia

In this paper, we propose a new definition of stable $(r + 1)$ -th capillary hypersurfaces from variational perspective for any $1 \leq r \leq n - 1$ . More precisely, we define stable $(r…

math.DG2025

Willmore-type inequality in unbounded convex sets

Xiaohan Jia, Guofang Wang, Chao Xia +1

In this paper we prove the following Willmore-type inequality: On an unbounded closed convex set $K \subset R^{n + 1}$ $(n \geq 2)$ , for any embedded hypersurface $I^£ \subset K$ …

math.DG2024

Monotonicity Formulas for Capillary Surfaces

Guofang Wang, Chao Xia, Xuwen Zhang

In this paper, we establish monotonicity formulas for capillary surfaces in the half-space $R_{+}^{3}$ and in the unit ball $B^{3}$ and extend the result of Volkmann (C…

Stable (r+1)-th capillary hypersurfaces

Willmore-type inequality in unbounded convex sets

Monotonicity Formulas for Capillary Surfaces

Stable $(r + 1)$ -th capillary hypersurfaces