8 citations · 12 across the 4 of their papers we have counts for
6 papers
The mean curvature flow of subgroups on Lie groups of dimension three
Romina M. Arroyo, Gabriela P. Ovando, Mariel Sáez
In this work we study the existence of solutions to the Mean Curvature Flow for which the initial condition has the structure of a two-dimensional Lie subgroup within a Lie group o…
The mean curvature flow on solvmanifolds
Romina M. Arroyo, Gabriela P. Ovando, Raquel Perales +1
This work is a survey of the most relevant background material to motivate and understand the construction and classification of translating solutions to mean curvature flow on a f…
The Hadamard formula and the Rayleigh-Faber-Krahn inequality for nonlocal eigenvalue problems
Rafael D. Benguria, Mariel Sáez, Marcone C. Pereira
In this paper we obtain a Hadamard type formula for simple eigenvalues and an analog to the Rayleigh-Faber-Krahn inequality for a class of nonlocal eigenvalue problems. Such class…
On the evolution by fractional mean curvature
Mariel Sáez, Enrico Valdinoci
In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction…
Some constructions for the fractional Laplacian on noncompact manifolds
Valeria Banica, Maria del Mar González, Mariel Sáez
We give a definition of the fractional Laplacian on some noncompact manifolds, through an extension problem introduced by Caffarelli-Silvestre. While this definition in the compact…
Evolution of convex lens-shaped networks under curve shortening flow
Oliver C. Schnürer, Abderrahim Azouani, Marc Georgi +8
We consider convex symmetric lens-shaped networks in R^2 that evolve under curve shortening flow. We show that the enclosed convex domain shrinks to a point in finite time. Further…