Zobrazeno 1 - 10
of 68
pro vyhledávání: '"Alencar, Hilário"'
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
We classify the $O(p)\times O(q)$-invariant constant mean curvature hypersurfaces with singularity at the origin, solving a conjecture of Wu-yi Hsiang.
Comment: 17 pages, 7 figures
Comment: 17 pages, 7 figures
Externí odkaz:
http://arxiv.org/abs/2402.09616
In this article, under mild constraints on the sectional curvature, we exploit a divergence formula for symmetric endomorphisms to deduce a general Poincar\'e type inequality. We apply such inequality to higher-order mean curvature of hypersurfaces o
Externí odkaz:
http://arxiv.org/abs/2203.10334
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
Autor:
Alencar, Hilário, Neto, Gregório Silva
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. These results were generalized by S. S. Chern, and then by Eschenburg and Tribuzy, fo
Externí odkaz:
http://arxiv.org/abs/2203.06206
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
Publikováno v:
Results Math. 78 (2023), no. 4, Paper No. 125, 16 pp
In this paper we prove rigidity results for the sphere, the plane and the right circular cylinder as the only self-shrinkers satisfying a classic geometric assumption, namely the union of all tangent affine submanifolds of a complete self-shrinker om
Externí odkaz:
http://arxiv.org/abs/2012.07104
In this paper we prove rigidity results for two-dimensional, closed, immersed, non-necessarily convex, self-similar solutions of a wide class of fully non-linear parabolic flows in $\mathbb{R}^3$. We show this self-similar solutions are the round sph
Externí odkaz:
http://arxiv.org/abs/2009.10494