Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Moller, Niels Martin"'
We prove a rigidity result for mean curvature self-translating solitons, characterizing the grim reaper cylinder as the only finite entropy self-translating 2-surface in $\mathbb{R}^3$ of width $\pi$ and bounded from below. The proof makes use of par
Externí odkaz:
http://arxiv.org/abs/2304.11953
We study translating solitons for the mean curvature flow, $\Sigma^2\subseteq\mathbb{R}^3$ which are contained in slabs, and are of finite genus and finite entropy. As a first consequence of our results, we can enumerate connected components of slice
Externí odkaz:
http://arxiv.org/abs/2209.01640
In this work, we study the space of complete embedded rotationally symmetric self-shrinking hypersurfaces in $\mathbb{R}^{n+1}$. First, using comparison geometry in the context of metric geometry, we derive explicit upper bounds for the entropy of al
Externí odkaz:
http://arxiv.org/abs/2202.08641
Autor:
Chini, Francesco, Møller, Niels Martin
We study properly immersed ancient solutions of the codimension one mean curvature flow in $n$-dimensional Euclidean space, and classify the convex hulls of the subsets of space reached by any such flow. In particular, it follows that any compact con
Externí odkaz:
http://arxiv.org/abs/1901.05481
Autor:
Chini, Francesco, Møller, Niels Martin
While it is well known from examples that no interesting `halfspace theorem' holds for properly immersed complete $n$-dimensional self-translating mean curvature flow solitons in Euclidean space $\mathbb{R}^{n+1}$, we show that they must all obey a g
Externí odkaz:
http://arxiv.org/abs/1809.01069
Autor:
Møller, Niels Martin
This paper establishes geometric obstructions to the existence of complete, properly embedded, mean curvature flow self-translating solitons $\Sigma^n\subseteq \mathbb{R}^{n+1}$, generalizing previously known non-existence conditions such as cylindri
Externí odkaz:
http://arxiv.org/abs/1411.2319
For fixed large genus, we construct families of complete immersed minimal surfaces in R3 with four ends and dihedral symmetries. The families exist for all large genus and at an appropriate scale degenerate to the plane.
Comment: 45 page, 1 figu
Comment: 45 page, 1 figu
Externí odkaz:
http://arxiv.org/abs/1409.8381
Autor:
Møller, Niels Martin
We construct many closed, embedded mean curvature self-shrinking surfaces $\Sigma_g^2\subseteq\mathbb{R}^3$ of high genus $g=2k$, $k\in \mathbb{N}$. Each of these shrinking solitons has isometry group equal to the dihedral group on $2g$ elements, and
Externí odkaz:
http://arxiv.org/abs/1111.7318
Publikováno v:
J. Reine Angew. Math. 739 (2018), 1--39. MR3808256
We give the first rigorous construction of complete, embedded self-shrinking hypersurfaces under mean curvature flow, since Angenent's torus in 1989. The surfaces exist for any sufficiently large prescribed genus $g$, and are non-compact with one end
Externí odkaz:
http://arxiv.org/abs/1106.5454
Publikováno v:
Trans. Amer. Math. Soc. 366 (2014), no. 8, 3943--3963. MR3206448
In this paper we present a new family of non-compact properly embedded, self-shrinking, asymptotically conical, positive mean curvature ends $\Sigma^n\subseteq\mathbb{R}^{n+1}$ that are hypersurfaces of revolution with circular boundaries. These hype
Externí odkaz:
http://arxiv.org/abs/1008.1609