Álvaro Ramos

Dynamical Stability of Translating Solitons to Mean Curvature Flow in Hyperbolic Space

Ronaldo F. de Lima, Álvaro Ramos

We develop the theory of translating solitons for the Mean Curvature Flow (MCF) in hyperbolic space of dimension $n+1\ge 3$. More specifically, we establish that horospheres are dynamically stable as radial graphical solutions to MCF. To that end, we construct rotationally invariant …

Dynamical Stability of Translating Solitons to Mean Curvature Flow in Hyperbolic Space

Ronaldo F. de Lima, Álvaro Ramos

We develop the theory of translating solitons for the Mean Curvature Flow (MCF) in hyperbolic space of dimension $n+1\ge 3$. More specifically, we establish that horospheres are dynamically stable as radial graphical solutions to MCF. To that end, we construct rotationally invariant …

Solitons to mean curvature flow in the hyperbolic 3-space

Ronaldo F. de Lima, Álvaro Ramos, Joao Paulo Dos Santos

We consider translators (i.e., initial condition of translating solitons) to mean curvature flow (MCF) in the hyperbolic 3 -space \mathbb{H}^{3} , providing existence and classification results. More specifically, we show the existence and uniqueness of two distinct one-parameter families of complete translators …

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Totally umbilic surfaces in hyperbolic 3-manifolds of finite volume

Colin Adams, William H. Meeks, Álvaro Ramos

Abstract: For every connected surface $S$ of finite negative Euler characteristic and every $H\in [0,1)$, we construct a hyperbolic 3-manifold $N(S,H)$ of finite volume and a proper, two-sided, totally umbilic embedding $f\colon S\to N(S,H)$ with mean curvature $H$. Conversely, we prove that …

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

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

We establish the existence of one-parameter families of helicoidal surfaces of $\mathbb H^2\times\mathbb R$ which, under mean curvature flow, simultaneously rotate about a vertical axis and translate vertically.

On the non-parabolicity of $Sol_3$

Leonardo Bonorino, Giovanni Nunes, Álvaro Ramos, Jaime Ripoll et autres

We prove that $Sol_3$, the isometry group of the Minkowski plane, is non parabolic with respect to any left invariant metric.

La impresionante diversidad y estructura del bosque tropical a través de una gradiente altitudinal en la selva central del Perú

Abel Lorenzo Monteagudo, María Villalba, Nadir Pallqui, Oliver Lawrence Phillips et autres

Los bosques pre-montanos y montanos son poco estudiados y su composición florística es muy poco conocida, aunque últimamente aquí se han descubierto nuevas especies de árboles. Describimos la diversidad, composición florística y estructura del bosque en 13 parcelas permanentes de 1 ha, …

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Modifications preserving hyperbolicity of link complements

Colin Adams, William H. Meeks, Álvaro Ramos

Given a link in a 3-manifold such that the complement is hyperbolic, we provide two modifications to the link, called the chain move and the switch move, that preserve hyperbolicity of the complement, with only a relatively small number of manifold-link pair …

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All the President’s Lies: How Brazilian News Media Addressed False and Inaccurate Claims in Their Titles

Marília Gehrke, Marcelo Träsel, Álvaro Ramos, Júlia Ozorio

This paper examines how the Brazilian media covered false and misleading claims made by President Jair Bolsonaro in the first year of the Covid-19 pandemic. To do so, we extracted titles from 111 news articles connected to twenty-one disinformation episodes. The texts …

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Geometrization in Geometry

Izabella Muraro de Freitas, Álvaro Ramos

So far, the most magnificent breakthrough in mathematics in the 21st century is the Geometrization Theorem, a bold conjecture by William Thurston (generalizing Poincaré's Conjecture) and proved by Grigory Perelman, based on the program suggested by Richard Hamilton. In this survey article, …

Geometrization in Geometry

Izabella de Freitas, Álvaro Ramos

So far, the most magnificent breakthrough in mathematics in the 21st century is the Geometrization Theorem, a bold conjecture by William Thurston (generalizing Poincaré's Conjecture) and proved by Grigory Perelman, based on the program suggested by Richard Hamilton.In this survey article, we …

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Elliptic Weingarten Hypersurfaces of Riemannian Products

Ronaldo F. de Lima, Álvaro Ramos, João Paulo 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 $M\times\mathbb R$, which are those whose principal curvatures $k_1,\dots ,k_n$ and angle function $θ$ satisfy a relation $W(k_1,\dots,k_n,θ^2)=0,$ being $W$ …