Zobrazeno 1 - 10
of 19
pro vyhledávání: '"53E10, 53C42"'
We consider the volume preserving flow of smooth, closed and convex hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1}$ with speed given by a general nonhomogeneous function of the Gauss curvature. For a large class of speed functions, we prove
Externí odkaz:
http://arxiv.org/abs/2406.05159
In this paper, we prove gap results for complete self-shrinkers of the $r$-mean curvature flow involving a modified second fundamental form. These results extend previous results for self-shrinkers of the mean curvature flow due to Cao-Li and Cheng-P
Externí odkaz:
http://arxiv.org/abs/2402.09627
Autor:
Kwong, Kwok-Kun, Wei, Yong
Publikováno v:
Advances in Mathematics, Vol. 430, 1 Oct 2023, article no. 109213
In this paper, we establish two families of sharp geometric inequalities for closed hypersurfaces in space forms or other warped product manifolds. Both families of inequalities compare three distinct geometric quantities. The first family concerns t
Externí odkaz:
http://arxiv.org/abs/2303.00930
In 1951, H. Hopf proved that the only surfaces, homeomorphic to the sphere, with constant mean curvature in the Euclidean space are the round (geometrical) spheres. In this paper we survey some contributions of Renato Tribuzy to generalize the result
Externí odkaz:
http://arxiv.org/abs/2203.06270
Autor:
Alencar, Hilário, Neto, Gregório Silva
In this paper we prove that two-dimensional translating solitons in $\mathbb{R}^3$ with finite $L$-index are homeomorphic to a plane or a cylinder and that a two-dimensional self-expander with finite $L$-index and sub exponential weighted volume grow
Externí odkaz:
http://arxiv.org/abs/2203.06214
This paper studies rigidity for immersed self-shrinkers of the mean curvature flow of surfaces in the three-dimensional Euclidean space $\mathbb{R}^3.$ We prove that an immersed self-shrinker with finite $L$-index must be proper and of finite topolog
Externí odkaz:
http://arxiv.org/abs/2106.09165
Autor:
Zhu, Jonathan J.
We prove {\L}ojasiewicz inequalities for round cylinders and cylinders over Abresch-Langer curves, using perturbative analysis of a quantity introduced by Colding-Minicozzi. A feature is that this auxiliary quantity allows us to work essentially at f
Externí odkaz:
http://arxiv.org/abs/2101.09025
Autor:
Sun, Ao, Zhu, Jonathan J.
We show that the product of two round shrinking spheres is an isolated self-shrinker in any codimension, modulo rotations. Moreover we prove explicit {\L}ojasiewicz inequalities near such products. {\L}ojasiewicz inequalities were previously used by
Externí odkaz:
http://arxiv.org/abs/2011.01636
Autor:
Zhu, Jonathan J.
We establish {\L}ojasiewicz inequalities for a class of cylindrical self-shrinkers for the mean curvature flow, which includes round cylinders and cylinders over Abresch-Langer curves, in any codimension. We deduce the uniqueness of blowups at singul
Externí odkaz:
http://arxiv.org/abs/2011.01633
In 1951, H. Hopf proved that the only surfaces, homeomorphic to the sphere, with constant mean curvature in the Euclidean space are the round (geometrical) spheres. In this paper we survey some contributions of Renato Tribuzy to generalize the result
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9580cf29671c28d1fdc5ad2c77f3fbc7
http://arxiv.org/abs/2203.06270
http://arxiv.org/abs/2203.06270