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Autor:
Hershkovits, Or, Senatore, Leonardo
We study mean convex mean curvature flow $M_s$ of local spacelike graphs in the flat slicing of de Sitter space. We show that if the initial slice is of non-negative time and is graphical over a large enough ball, and if $M_s$ is of bounded mean curv
Externí odkaz:
http://arxiv.org/abs/2307.11504
We consider the profile function of ancient ovals and of noncollapsed translators. Recall that pioneering work of Angenent-Daskalopoulos-Sesum (JDG '19, Annals '20) gives a sharp $C^0$-estimate and a quadratic concavity estimate for the profile funct
Externí odkaz:
http://arxiv.org/abs/2305.19137
Publikováno v:
In Advances in Mathematics September 2024 453
In this paper, we classify all noncollapsed singularity models for the mean curvature flow of 3-dimensional hypersurfaces in $\mathbb{R}^4$ or more generally in $4$-manifolds. Specifically, we prove that every noncollapsed translating hypersurface in
Externí odkaz:
http://arxiv.org/abs/2105.13819
Some of the most worrisome potential singularity models for the mean curvature flow of $3$-dimensional hypersurfaces in $\mathbb{R}^4$ are noncollapsed wing-like flows, i.e. noncollapsed flows that are asymptotic to a wedge. In this paper, we rule ou
Externí odkaz:
http://arxiv.org/abs/2105.13100
We study, using Mean Curvature Flow methods, 3+1 dimensional cosmologies with a positive cosmological constant, matter satisfying the dominant and the strong energy conditions, and with spatial slices that can be foliated by 2-dimensional surfaces th
Externí odkaz:
http://arxiv.org/abs/2004.10754
In this paper, we introduce a version of the moving plane method that applies to potentially quite singular hypersurfaces, generalizing the classical moving plane method for smooth hypersurfaces. Loosely speaking, our version for varifolds shows that
Externí odkaz:
http://arxiv.org/abs/2003.01505
Publikováno v:
In Advances in Mathematics 1 December 2023 434
It is a fundamental open problem for the mean curvature flow, and in fact for many partial differential equations, whether or not all blowup limits are selfsimilar. In this short note, we prove that for the mean curvature flow of mean convex surfaces
Externí odkaz:
http://arxiv.org/abs/1910.02341