We study $\lambda $-hypersurfaces that are critical points of a Gaussian weighted area
functional $\int _ {\Sigma} e^{-\frac {| x|^ 2}{4}} dA $ for compact variations that preserve …

Let $\Omega\subset\Bbb {R}^{n+ 1} $ have minimal Gaussian surface area among all sets
satisfying $\Omega=-\Omega $ with fixed Gaussian volume. Let $ A= A_x $ be the second …

In this paper, we firstly verify that if M n is an n-dimensional complete self-shrinker with
polynomial volume growth in ℝ n+ 1, and if the squared norm of the second fundamental …

In this paper, we obtain several new characterizations of the Clifford torus as a Lagrangian
self-shrinker. We first show that the Clifford torus S^ 1 (1) * S^ 1 (1) S 1 (1)× S 1 (1) is the …

We study singularity models of mean curvature flow (" MCF") and their generalizations. In the
first part, we focus on rigidity and curvature estimates for self-shrinkers. We give a rigidity …

We obtain an infinite family of complete non embedded rotational surfaces in $\mathbb R^
3$ whose second fundamental forms have length equal to one at any point. Also we prove …

Neste trabalho apresentamos um estudo dos sólitons de fluxo de curvatura média, baseado
no trabalho de Alías, Lira e Rigoli, onde introduziram o conceito de sólitons do fluxo de …

O Fluxo de curvatura média aparece na literatura, por volta dos anos 50, na modelagem de
fronteiras de grãos que se formam durante a cristalização em processos de fundição …

We obtain an infinite family of complete non embedded rotational surfaces in $\mathbb {R}^
3$ whose second fundamental forms have length equal to one at any point. Also we prove …