Zobrazeno 1 - 10
of 34
pro vyhledávání: '"Ilmanen, Tom"'
Autor:
Ilmanen, Tom, White, Brian
For each $g\ge 3$, we prove existence of a compact, connected, smoothly embedded, genus-$g$ surface $M_g$ with the following property: under mean curvature flow, there is exactly one singular point at the first singular time, and the tangent flow at
Externí odkaz:
http://arxiv.org/abs/2406.18703
The purpose of these notes is to provide an introduction to those who want to learn more about translating solitons for the mean curvature flow in $\mathbb{R}^3$, particularly those which are complete graphs over domains in $\mathbb{R}^2$. In this pa
Externí odkaz:
http://arxiv.org/abs/1901.09101
In this paper we provide a full classification of complete translating graphs in $\mathbf{R}^3$. We also construct two $(n-1)$-parameter families of new examples of translating graphs in $\mathbf{R}^{n+1}$.
Comment: 29 pages, 3 Figures. A few ty
Comment: 29 pages, 3 Figures. A few ty
Externí odkaz:
http://arxiv.org/abs/1805.10860
We prove the existence of the flow by curvature of regular planar networks starting from an initial network which is non-regular. The proof relies on a monotonicity formula for expanding solutions and a local regularity result for the network flow in
Externí odkaz:
http://arxiv.org/abs/1407.4756
Shrinkers are special solutions of mean curvature flow (MCF) that evolve by rescaling and model the singularities. While there are infinitely many in each dimension, [CM1] showed that the only generic are round cylinders $\SS^k\times \RR^{n-k}$. We p
Externí odkaz:
http://arxiv.org/abs/1304.6356
The entropy of a hypersurface is a geometric invariant that measures complexity and is invariant under rigid motions and dilations. It is given by the supremum over all Gaussian integrals with varying centers and scales. It is monotone under mean cur
Externí odkaz:
http://arxiv.org/abs/1205.2043
Autor:
Ilmanen, Tom, White, Brian
Publikováno v:
Camb. J. Math. 3 (2015), 1--18
We prove that the density of a topologically nontrivial, area-minimizing hypercone with an isolated singularity must be greater than the square root of 2. The Simons' cones show that this is the best possible constant. If one of the components of the
Externí odkaz:
http://arxiv.org/abs/1010.5068
Autor:
Ilmanen, Tom, Sesum, Natasa
We study the flow $M_t$ of a smooth, strictly convex hypersurface by its mean curvature in $\mathrm{R}^{n+1}$. The surface remains smooth and convex, shrinking monotonically until it disappears at a critical time $T$ and point $x^*$ (which is due to
Externí odkaz:
http://arxiv.org/abs/math/0502530
Perelman has discovered two integral quantities, the shrinker entropy $\cW$ and the (backward) reduced volume, that are monotone under the Ricci flow $\pa g_{ij}/\pa t=-2R_{ij}$ and constant on shrinking solitons. Tweaking some signs, we find similar
Externí odkaz:
http://arxiv.org/abs/math/0405036