Zobrazeno 1 - 10
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pro vyhledávání: '"XIA, Chao"'
In the paper we establish an optimal logarithmic Sobolev inequality for complete, non-compact, properly embedded self-shrinkers in the Euclidean space, which generalizes a recent result of Brendle \cite{Brendle22} for closed self-shrinkers. We first
Externí odkaz:
http://arxiv.org/abs/2410.13601
In this paper we prove the following Willmore-type inequality: On an unbounded closed convex set $K\subset\mathbb{R}^{n+1}$ $(n\ge 2)$, for any embedded hypersurface $\Sigma\subset K$ with boundary $\partial\Sigma\subset \partial K$ satisfying certai
Externí odkaz:
http://arxiv.org/abs/2409.03321
In this paper, we establish monotonicity formulas for capillary surfaces in the half-space $\mathbb{R}^3_+$ and in the unit ball $\mathbb{B}^3$ and extend the result of Volkmann (Comm. Anal. Geom.24(2016), no.1, 195~221. \href{https://doi.org/10.4310
Externí odkaz:
http://arxiv.org/abs/2409.03314
In this paper, we provide an affirmative answer to [16, Conjecture 1.5] on the Alexandrov-Fenchel inequality for quermassintegrals for convex capillary hypersurfaces in the Euclidean half-space. More generally, we establish a theory for capillary con
Externí odkaz:
http://arxiv.org/abs/2408.13655
In this note, we study a Serrin-type partially overdetermined problem proposed by Guo-Xia (Calc. Var. Partial Differential Equations 58: no. 160, 2019. https://doi.org/10.1007/s00526-019-1603-3, and prove a rigidity result that characterizes capillar
Externí odkaz:
http://arxiv.org/abs/2311.18581
Publikováno v:
Calc. Var. Partial Differential Equations 63 (2024), no.5, Paper No. 125, 24 pp
In this paper, we first prove a rigidity result for a Serrin-type partially overdetermined problem in the half-space, which gives a characterization of capillary spherical caps by the overdetermined problem. In the second part, we prove quantitative
Externí odkaz:
http://arxiv.org/abs/2311.18585
Copy-move forgery detection aims at detecting duplicated regions in a suspected forged image, and deep learning based copy-move forgery detection methods are in the ascendant. These deep learning based methods heavily rely on synthetic training data,
Externí odkaz:
http://arxiv.org/abs/2311.13263
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 $(r+1)$-th capillary hypersurfaces to be smooth local minimizers of a new
Externí odkaz:
http://arxiv.org/abs/2311.11333
Publikováno v:
J. Math. Study 57 (2024), no. 3, 243-258. Special Issue on the 100th Anniversary of the Founding of the Mathematics Discipline at Xiamen University
In this paper, we prove an optimal Heintze-Karcher-type inequality for anisotropic free boundary hypersurfaces in general convex domains. The equality is achieved for anisotropic free boundary Wulff shapes in a convex cone. As applications, we prove
Externí odkaz:
http://arxiv.org/abs/2311.01162
In this paper, we derive general monotone quantities and geometric inequalities associated with $p$-capacitary functions in asymptotically flat $3$-manifolds with simple topology and nonnegative scalar curvature. The inequalities become equalities on
Externí odkaz:
http://arxiv.org/abs/2306.00744