Zobrazeno 1 - 10
of 365
pro vyhledávání: '"53e10"'
Obstructions to the existence of spacelike solitons depending on the growth of the mean curvature $H$ are proved for Lorentzian products $(M\times \mathbb{R}, \bar g=g_M-dt^2)$ with lowerly bounded curvature. The role of these bounds for both the com
Externí odkaz:
http://arxiv.org/abs/2412.10330
Autor:
Guo, Siao-Hao
The level set flow of a mean-convex closed hypersurface is stable off singularities, in the sense that the level set flow of the perturbed hypersurface would be close in the smooth topology to the original flow wherever the latter is regular. To stud
Externí odkaz:
http://arxiv.org/abs/2412.08977
In this paper we introduce the target flow -- a specific curve shortening flow with an ambient forcing term -- that, given an embedded (not necessarily convex) target curve, will attempt to evolve a given source curve to that target. The motivation f
Externí odkaz:
http://arxiv.org/abs/2411.18951
Autor:
Liu, Yuning, Tonegawa, Yoshihiro
Suppose that a closed $1$-rectifiable set $\Gamma_0\subset \mathbb R^2$ of finite $1$-dimensional Hausdorff measure and a vector field $u$ in a dimensionally critical Sobolev space are given. It is proved that, starting from $\Gamma_0$, there exists
Externí odkaz:
http://arxiv.org/abs/2411.18284
We study the gradient flow of the Allen-Cahn equation with fixed boundary contact angle in Euclidean domains for initial data with bounded energy. Under general assumptions, we establish both interior and boundary convergence properties for the solut
Externí odkaz:
http://arxiv.org/abs/2411.17979
We complete the classification of semigraphical translators for mean curvature flow in $\mathbb{R}^3$ that was initiated by Hoffman-Mart\'in-White. Specifically, we show that there is no solution to the translator equation on the upper half-plane wit
Externí odkaz:
http://arxiv.org/abs/2411.16889
Autor:
Lagacé, Jean, Lynch, Stephen
We introduce a new curvature condition for high-codimension submanifolds of a Riemannian ambient space, called quasi-parallel mean curvature (QPMC). The class of submanifolds with QPMC includes all CMC hypersurfaces and submanifolds with parallel mea
Externí odkaz:
http://arxiv.org/abs/2411.14340
Autor:
Fong, Frederick Tsz-Ho
In this article, we establish some uniqueness and symmetry results of self-similar solutions to curvature flows by some homogeneous speed functions of principal curvatures in some warped product spaces. In particular, we proved that any compact star-
Externí odkaz:
http://arxiv.org/abs/2411.08198
In this work the evolution of a fluid droplet in vacuum is considered. This means that the surface tension and the fluid forces are in equilibrium at the free boundary. The fluid is governed by the incompressible quasi-steady Stokes equation. We pres
Externí odkaz:
http://arxiv.org/abs/2411.06940
We rigorously show that a large family of monotone quantities along the weak inverse mean curvature flow is the limit case of the corresponding ones along the level sets of $p$-capacitary potentials. Such monotone quantities include Willmore and Mink
Externí odkaz:
http://arxiv.org/abs/2411.06462