Zobrazeno 1 - 10
of 80
pro vyhledávání: '"Perales, Raquel"'
We establish a nonlinear analogue of a splitting map into a Euclidean space, as a harmonic map into a flat torus. We prove that the existence of such a map implies Gromov-Hausdorff closeness to a flat torus in any dimension. Furthermore, Gromov-Hausd
Externí odkaz:
http://arxiv.org/abs/2311.01342
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 family of solvmanifolds. We introduce the mean curvature flow and some
Externí odkaz:
http://arxiv.org/abs/2305.02378
The rigidity of the Riemannian positive mass theorem for asymptotically hyperbolic manifolds states that the total mass of such a manifold is zero if and only if the manifold is isometric to the hyperbolic space. This leads to study the stability of
Externí odkaz:
http://arxiv.org/abs/2304.08443
Autor:
Del Nin, Giacomo, Perales, Raquel
We prove that given an $n$-dimensional integral current space and a $1$-Lipschitz map, from this space onto the $n$-dimensional Euclidean ball, that preserves the mass of the current and is injective on the boundary, then the map has to be an isometr
Externí odkaz:
http://arxiv.org/abs/2210.06406
The concept of the capacity of a compact set in $\mathbb R^n$ generalizes readily to noncompact Riemannian manifolds and, with more substantial work, to metric spaces (where multiple natural definitions of capacity are possible). Motivated by analyti
Externí odkaz:
http://arxiv.org/abs/2204.09732
Publikováno v:
Calc. Var. Partial Differential Equations 62 (2023) Paper No. 26, 34 pp
Using variational methods together with symmetries given by singular Riemannian foliations with positive dimensional leaves, we prove the existence of an infinite number of sign-changing solutions to Yamabe type problems, which are constant along the
Externí odkaz:
http://arxiv.org/abs/2202.13109
Publikováno v:
In Nonlinear Analysis December 2024 249
Publikováno v:
Comment. Math. Helv. 97 (2022), no. 3, 555--609
We prove an upper bound on the rank of the abelianised revised fundamental group (called "revised first Betti number") of a compact $RCD^{*}(K,N)$ space, in the same spirit of the celebrated Gromov-Gallot upper bound on the first Betti number for a s
Externí odkaz:
http://arxiv.org/abs/2104.06208
We prove results on intrinsic flat convergence of points---a concept first explored by Sormani in \cite{Sormani-AA}. In particular, we discuss compatibility with Gromov-Hausdorff convergence of points---a concept first described by Gromov in \cite{Gr
Externí odkaz:
http://arxiv.org/abs/2010.07885
Autor:
Allen, Brian, Perales, Raquel
Given a compact, connected, and oriented manifold with boundary $M$ and a sequence of smooth Riemannian metrics defined on it, $g_j$, we prove volume preserving intrinsic flat convergence of the sequence to the smooth Riemannian metric $g_0$ provided
Externí odkaz:
http://arxiv.org/abs/2006.13030