Willmore‐type inequality in unbounded convex sets
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract In this paper, we prove the following Willmore‐type inequality: on an unbounded closed convex set K⊂Rn+1$K\subset \mathbb {R}^{n+1}$ (n⩾2$(n\geqslant 2$), for any embedded hypersurface Σ⊂K${\Sigma }\subset K$ with boundary ∂Σ⊂∂K$\partial {\Sigma }\subset \partial K$ satisfying a certain contact angle condition, there holds 1n+1∫ΣHndA⩾AVR(K)|Bn+
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