Zobrazeno 1 - 10
of 79
pro vyhledávání: '"SEMOLA, DANIELE"'
Let $(M^n,g)$ be a complete Riemannian manifold which is not isometric to $\mathbb{R}^n$, has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature decay. We prove that there is a set $\mathcal{G}\subset (0,\infty)$ wi
Externí odkaz:
http://arxiv.org/abs/2406.07509
We investigate the topological regularity and stability of noncollapsed Ricci limit spaces $(M_i^n,g_i,p_i)\to (X^n,d)$. We confirm a conjecture proposed by Colding and Naber in dimension $n=4$, showing that the cross-sections of tangent cones at a g
Externí odkaz:
http://arxiv.org/abs/2405.03839
We extend our previous work by building a smooth complete manifold $(M^6,g,p)$ with $\mathrm{Ric}\geq 0$ and whose fundamental group $\pi_1(M^6)=\mathbb{Q}/\mathbb{Z}$ is infinitely generated. The example is built with a variety of interesting geomet
Externí odkaz:
http://arxiv.org/abs/2311.12155
The goal of this paper is to establish a monotonicity formula for perimeter minimizing sets in RCD(0,N) metric measure cones, together with the associated rigidity statement. The applications include sharp Hausdorff dimension estimates for the singul
Externí odkaz:
http://arxiv.org/abs/2307.06205
Publikováno v:
Geom. Topol. 28 (2024) 3961-3972
Let $(M^n_i, g_i)\to (X,d_X)$ be a Gromov-Hausdorff converging sequence of Riemannian manifolds with ${\rm Sec}_{g_i} \ge -1$, ${\rm diam}\, (M_i)\le D$, and such that the $M^n_i$ are all homeomorphic to tori $T^n$. Then $X$ is homeomorphic to a $k$-
Externí odkaz:
http://arxiv.org/abs/2307.03824
It was conjectured by Milnor in 1968 that the fundamental group of a complete manifold with nonnegative Ricci curvature is finitely generated. The main result of this paper is a counterexample, which provides an example $M^7$ with ${\rm Ric}\geq 0$ s
Externí odkaz:
http://arxiv.org/abs/2303.15347
We show that several different interpretations of the inequality $\Delta f\leq\eta$ are equivalent in the setting of $\mathrm{RCD}(K,N)$ spaces. With respect to previously available results in this direction, we improve both on the generality of the
Externí odkaz:
http://arxiv.org/abs/2302.05474
This paper studies sharp and rigid isoperimetric comparison theorems and asymptotic isoperimetric properties for small and large volumes on $N$-dimensional ${\rm RCD}(K,N)$ spaces $(X,\mathsf{d},\mathscr{H}^N)$. Moreover, we obtain almost regularity
Externí odkaz:
http://arxiv.org/abs/2208.03739
Publikováno v:
Geom. Funct. Anal. 33, 593-636 (2023)
We solve a conjecture raised by Kapovitch, Lytchak, and Petrunin by showing that the metric measure boundary is vanishing on any ${\rm RCD}(K,N)$ space without boundary. Our result, combined with [Kapovitch-Lytchak-Petrunin '21], settles an open ques
Externí odkaz:
http://arxiv.org/abs/2205.10609
Autor:
Mondino, Andrea, Semola, Daniele
We establish Lipschitz regularity of harmonic maps from $\mathrm{RCD}(K,N)$ metric measure spaces with lower Ricci curvature bounds and dimension upper bounds in synthetic sense with values into $\mathrm{CAT}(0)$ metric spaces with non-positive secti
Externí odkaz:
http://arxiv.org/abs/2202.01590