R. D. de Lima

activity

20172024

collaborators

8 papers

math.DG2024

Rotators-Translators to Mean Curvature Flow in $H^{2} \times R$

Ronaldo F. de Lima, Álvaro K. Ramos, João Paulo dos Santos

We establish the existence of one-parameter families of helicoidal surfaces of $H^{2} \times R$ which, under mean curvature flow, simultaneously rotate about a vertical…

math.DG2023

Solitons to Mean Curvature Flow in the hyperbolic 3-space

R. F. de Lima, A. K. Ramos, J. P. dos Santos

We consider {translators} (i.e., initial condition of translating solitons) to mean curvature flow (MCF) in the hyperbolic $3$ -space $H^{3}$ , providing existence and classifi…

math.DG2023

A Survey on Convex Hypersurfaces of Riemannian Manifolds

Ronaldo Freire de Lima

We survey the main extensions of the classical Hadamard, Liebmann and Cohn-Vossen rigidity theorems on convex surfaces of $3$ -Euclidean space to the context of convex hypersurfaces…

math.DG2023

On Stability and Isoperimetry of Constant Mean Curvature Spheres of $H^{n} \times R$ and $S^{n} \times R .$

Ronaldo F. de Lima, Maria F. Elbert, Barbara Nelli

We approach the one-parameter family of rotational constant mean curvature (CMC) spheres of $H^{n} \times R$ and $S^{n} \times R$ focusing on their stabilit…

math.DG2022

Translators to Higher Order Mean Curvature Flows in $R^{n} \times R$ and $H^{n} \times R$

Ronaldo F. de Lima, Giuseppe Pipoli

We consider translators to the extrinsic flows in $R^{n} \times R$ and $H^{n} \times R$ (called $r$ -mean curvature flows or $r$ -MCF, for short) whose veloci…

math.DG2021

Einstein Hypersurfaces of Warped Product Spaces

Ronaldo F. de Lima, Fernando Manfio, João P. dos Santos

We consider Einstein hypersurfaces of warped products $I \times_{ω} Q_{ε}^{n},$ where $I \subset R$ is an open interval and $Q_{ε}^{n}$ is the simply connected space form…

math.DG2021

Elliptic Weingarten Hypersurfaces of Riemannian Products

Ronaldo F. de Lima, Álvaro K. Ramos, João P. dos Santos

Let $M^{n}$ be either a simply connected space form or a rank-one symmetric space of noncompact type. We consider Weingarten hypersurfaces of $M \times R$ , which are those whos…

math.DG2017

Convexity, Rigidity, and Reduction of Codimension of Isometric Immersions into Space Forms

Ronaldo F. de Lima, Rubens L. de Andrade

We consider isometric immersions of complete connected Riemannian manifolds into space forms of nonzero constant curvature. We prove that if such an immersion is compact and has se…

Rotators-Translators to Mean Curvature Flow in H2×R

Solitons to Mean Curvature Flow in the hyperbolic 3-space

A Survey on Convex Hypersurfaces of Riemannian Manifolds

On Stability and Isoperimetry of Constant Mean Curvature Spheres of Hn×R and Sn×R.

Translators to Higher Order Mean Curvature Flows in Rn×R and Hn×R

Einstein Hypersurfaces of Warped Product Spaces

Elliptic Weingarten Hypersurfaces of Riemannian Products

Convexity, Rigidity, and Reduction of Codimension of Isometric Immersions into Space Forms

Rotators-Translators to Mean Curvature Flow in $H^{2} \times R$

On Stability and Isoperimetry of Constant Mean Curvature Spheres of $H^{n} \times R$ and $S^{n} \times R .$

Translators to Higher Order Mean Curvature Flows in $R^{n} \times R$ and $H^{n} \times R$