Zobrazeno 1 - 10
of 130 807
pro vyhledávání: '"Alexandrov, AS"'
Autor:
Kwong, Kwok-Kun, Wei, Yong
In this paper, we derive new sharp weighted Alexandrov-Fenchel and Minkowski inequalities for smooth, closed hypersurfaces under various convexity assumptions in Euclidean, spherical, and hyperbolic spaces. These inequalities extend classical results
Externí odkaz:
http://arxiv.org/abs/2412.08923
Autor:
Liu, Jian-Guo, Pego, Robert L.
We study all the ways that a given convex body in $d$ dimensions can break into countably many pieces that move away from each other rigidly at constant velocity, with no rotation or shearing. The initial velocity field is locally constant, but may b
Externí odkaz:
http://arxiv.org/abs/2411.05606
Alexandrov spaces are defined via axioms similar to those of the Euclid axioms but where certain equalities are replaced with inequalities. Depending on the signs of the inequalities, we obtain Alexandrov spaces with curvature bounded above (CBA) and
Autor:
Cygan, Wojciech, Grzywny, Tomasz
In this article we obtain a nonlocal version of the Alexandrov Theorem which asserts that the only set with sufficiently smooth boundary and of constant nonlocal mean curvature is an Euclidean ball. We consider a general nonlocal mean curvature given
Externí odkaz:
http://arxiv.org/abs/2410.10199
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
Autor:
Liu, Junbang
We prove an Alexandrov-Bakelman-Pucci type estimate, which involves the integral of the determinant of the complex Hessian over a certain subset. It improves the classical ABP estimate adapted (by inequality $2^{2n}|\det(u_{i\bar{j}})|^2\geq |\det(\n
Externí odkaz:
http://arxiv.org/abs/2410.04395
In this paper, an anisotropic volume-preserving mean curvature type flow for star-shaped anisotropic $\omega_0$-capillary hypersurfaces in the half-space is studied, and the long-time existence and smooth convergence to a capillary Wulff shape are ob
Externí odkaz:
http://arxiv.org/abs/2408.10740
Autor:
Santilli, Mario, Valentini, Paolo
In this paper we extend Alexandrov's sphere theorems for higher-order mean curvature functions to $ W^{2,n} $-regular hypersurfaces under a general degenerate elliptic condition. The proof is based on the extension of the Montiel-Ros argument to the
Externí odkaz:
http://arxiv.org/abs/2409.01061
We study the asymptotic behavior of the volume preserving mean curvature and the Mullins-Sekerka flat flow in three dimensional space. Motivated by this we establish a 3D sharp quantitative version of the Alexandrov inequality for $C^2$-regular sets
Externí odkaz:
http://arxiv.org/abs/2406.17691
Autor:
Mei, Xinqun, Weng, Liangjun
In this article, we first introduce the quermassintegrals for compact hypersurfaces with capillary boundaries in hyperbolic space from a variational viewpoint, and then we solve an isoperimetric type problem in hyperbolic space. By constructing a new
Externí odkaz:
http://arxiv.org/abs/2406.07304