Daniele Semola

activity

20182025

most citedAsymptotic isoperimetry on non collapsed spaces with lower Ricci bounds

32 citations · 123 across the 21 of their papers we have counts for

collaborators

23 papers

math.DG2025

Fukaya-Yamaguchi Conjecture in Dimension Four

Elia Bruè, Aaron Naber, Daniele Semola

Fukaya and Yamaguchi conjectured that if $M^{n}$ is a manifold with nonnegative sectional curvature, then the fundamental group is uniformly virtually abelian. In this short note we…

math.DG2025

Compact Manifolds with Unbounded Nilpotent Fundamental Groups and Positive Ricci Curvature

Elia Bruè, Aaron Naber, Daniele Semola

It follows from the work of Kapovitch and Wilking that a closed manifold with nonnegative Ricci curvature has an almost nilpotent fundamental group. Leftover questions and conjectu…

math.DG2024

Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature

Gioacchino Antonelli, Marco Pozzetta, Daniele Semola

Let $(M^{n}, g)$ be a complete Riemannian manifold which is not isometric to $R^{n}$ , has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature…

math.DG2024★ 3 cited

Topological regularity and stability of noncollapsed spaces with Ricci curvature bounded below

Elia Bruè, Alessandro Pigati, Daniele Semola

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 di…

math.DG2023

Six dimensional counterexample to the Milnor Conjecture

Elia Bruè, Aaron Naber, Daniele Semola

We extend our previous work by building a smooth complete manifold $(M^{6}, g, p)$ with $Ric \geq 0$ and whose fundamental group $π_{1} (M^{6}) = Q / Z$ is infinitely…

math.DG2023

Monotonicity formula and stratification of the singular set of perimeter minimizers in RCD spaces

Francesco Fiorani, Andrea Mondino, Daniele Semola

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 a…

math.DG2023★ 2 cited

Stability of Tori under Lower Sectional Curvature

Elia Brue, Aaron Naber, Daniele Semola

Let $(M_{i}^{n}, g_{i}) \to (X, d_{X})$ be a Gromov-Hausdorff converging sequence of Riemannian manifolds with $Sec_{g_{i}} \geq - 1$ , $diam (M_{i}) \leq D$ , and such that the $M_{i}^{n}$ …

math.DG2023★ 3 cited

Fundamental Groups and the Milnor Conjecture

Elia Bruè, Aaron Naber, Daniele Semola

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 co…

math.DG2023★ 4 cited

On the notion of Laplacian bounds on $RCD$ spaces and applications

Nicola Gigli, Andrea Mondino, Daniele Semola

We show that several different interpretations of the inequality $Δ f \leq η$ are equivalent in the setting of $RCD (K, N)$ spaces. With respect to previously available results…

math.DG2022★ 32 cited

Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds

Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta +1

This paper studies sharp and rigid isoperimetric comparison theorems and asymptotic isoperimetric properties for small and large volumes on $N$ -dimensional $RCD (K, N)$ spaces…

math.DG2022★ 4 cited

The metric measure boundary of spaces with Ricci curvature bounded below

Elia Bruè, Andrea Mondino, Daniele Semola

We solve a conjecture raised by Kapovitch, Lytchak, and Petrunin by showing that the metric measure boundary is vanishing on any $RCD (K, N)$ space without boundary. Our result…

math.DG2022★ 1 cited

Sharp isoperimetric comparison on non-collapsed spaces with lower Ricci bounds

Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta +1

This paper studies sharp isoperimetric comparison theorems and sharp dimensional concavity properties of the isoperimetric profile for non smooth spaces with lower Ricci curvature…

math.MG2021★ 1 cited

Constancy of the dimension in codimension one and locality of the unit normal on $RCD (K, N)$ spaces

Elia Bruè, Enrico Pasqualetto, Daniele Semola

The aim of this paper is threefold. We first prove that, on $RCD (K, N)$ spaces, the boundary measure of any set with finite perimeter is concentrated on the $n$ -regular set…

math.DG2021★ 5 cited

Weak Laplacian bounds and minimal boundaries in non-smooth spaces with Ricci curvature lower bounds

Andrea Mondino, Daniele Semola

The goal of the paper is four-fold. In the setting of non-smooth spaces with Ricci curvature lower bounds (more precisely RCD(K,N) metric measure spaces): - we develop an intrinsic…

math.MG2021★ 1 cited

Improved regularity estimates for Lagrangian flows on $RCD (K, N)$ spaces

Elia Bruè, Qin Deng, Daniele Semola

This paper gives a contribution to the study of regularity of Lagrangian flows on non-smooth spaces with lower Ricci curvature bounds. The main novelties with respect to the existi…

math.DG2020★ 2 cited

Boundary regularity and stability for spaces with Ricci bounded below

Elia Bruè, Aaron Naber, Daniele Semola

This paper studies the structure and stability of boundaries in noncollapsed $RCD (K, N)$ spaces, that is, metric-measure spaces $(X, d, H^{N})$ with lower Ricc…

math.FA2020★ 9 cited

The equality case in Cheeger's and Buser's inequalities on $RCD$ spaces

Nicolò De Ponti, Andrea Mondino, Daniele Semola

We prove that the sharp Buser's inequality obtained in the framework of $RCD (1, \infty)$ spaces by the first two authors is rigid, i.e. equality is obtained if and only if…

math.MG2020★ 2 cited

Rectifiability of RCD(K,N) spaces via $δ$ -splitting maps

Elia Bruè, Enrico Pasqualetto, Daniele Semola

In this note we give new proofs of rectifiability of RCD(K,N) spaces as metric measure spaces and lower semicontinuity of the essential dimension, via $δ$ -splitting maps. The argum…

math.FA2019★ 16 cited

Quantitative Obata's Theorem

Fabio Cavalletti, Andrea Mondino, Daniele Semola

We prove a quantitative version of Obata's Theorem involving the shape of functions with null mean value when compared with the cosine of distance functions from single points. The…

math.MG2019

Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces

Gioacchino Antonelli, Elia Bruè, Daniele Semola

The aim of this note is to generalize to the class of non collapsed RCD(K,N) metric measure spaces the volume bound for the effective singular strata obtained by Cheeger and Naber…

math.FA2018★ 26 cited

Polya-Szego inequality and Dirichlet $p$ -spectral gap for non-smooth spaces with Ricci curvature bounded below

Andrea Mondino, Daniele Semola

We study decreasing rearrangements of functions defined on (possibly non-smooth) metric measure spaces with Ricci curvature bounded below by $K > 0$ and dimension bounded above by $N…

math.MG2018★ 9 cited

Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows

Elia Bruè, Daniele Semola

We prove a regularity result for Lagrangian flows of Sobolev vector fields over RCD(K,N) metric measure spaces, regularity is understood with respect to a newly defined quasi-metri…

math.MG2018★ 3 cited

Regularity of Lagrangian flows over $R C D^{*} (K, N)$ spaces

Elia Bruè, Daniele Semola

The aim of this note is to provide regularity results for Regular Lagrangian flows of Sobolev vector fields over compact metric measure spaces verifying the Riemannian curvature di…

Fukaya-Yamaguchi Conjecture in Dimension Four

Compact Manifolds with Unbounded Nilpotent Fundamental Groups and Positive Ricci Curvature

Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature

Topological regularity and stability of noncollapsed spaces with Ricci curvature bounded below

Six dimensional counterexample to the Milnor Conjecture

Monotonicity formula and stratification of the singular set of perimeter minimizers in RCD spaces

Stability of Tori under Lower Sectional Curvature

Fundamental Groups and the Milnor Conjecture

On the notion of Laplacian bounds on RCD spaces and applications

Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds

The metric measure boundary of spaces with Ricci curvature bounded below

Sharp isoperimetric comparison on non-collapsed spaces with lower Ricci bounds

Constancy of the dimension in codimension one and locality of the unit normal on RCD(K,N) spaces

Weak Laplacian bounds and minimal boundaries in non-smooth spaces with Ricci curvature lower bounds

Improved regularity estimates for Lagrangian flows on RCD(K,N) spaces

Boundary regularity and stability for spaces with Ricci bounded below

The equality case in Cheeger's and Buser's inequalities on RCD spaces

Rectifiability of RCD(K,N) spaces via δ-splitting maps

Quantitative Obata's Theorem

Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces

Polya-Szego inequality and Dirichlet p-spectral gap for non-smooth spaces with Ricci curvature bounded below

Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows

Regularity of Lagrangian flows over RCD∗(K,N) spaces

On the notion of Laplacian bounds on $RCD$ spaces and applications

Constancy of the dimension in codimension one and locality of the unit normal on $RCD (K, N)$ spaces

Improved regularity estimates for Lagrangian flows on $RCD (K, N)$ spaces

The equality case in Cheeger's and Buser's inequalities on $RCD$ spaces

Rectifiability of RCD(K,N) spaces via $δ$ -splitting maps

Polya-Szego inequality and Dirichlet $p$ -spectral gap for non-smooth spaces with Ricci curvature bounded below

Regularity of Lagrangian flows over $R C D^{*} (K, N)$ spaces