Elia Brué

activity

20172026

most citedPositive solutions of transport equations and classical nonuniqueness of characteristic curves

51 citations · 248 across the 29 of their papers we have counts for

collaborators

34 papers

math.DG2026

Ollivier--Ricci Curvature on Groups of Polynomial Growth

Camillo Brena, Elia Bruè

We study Ollivier--Ricci curvature on Cayley graphs of groups of polynomial growth. Our main result shows that non-negative Ollivier--Ricci curvature forces the group to be virtual…

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★ 1 cited

Lower Ricci Curvature Bounds and the Orientability of Spaces

Camillo Brena, Elia Bruè, Alessandro Pigati

We study orientability in spaces with Ricci curvature bounded below. Building on the theory developed by Honda, we establish equivalent characterizations of orientability for Ricci…

math.AP2024

Flexibility of Two-Dimensional Euler Flows with Integrable Vorticity

Elia Bruè, Maria Colombo, Anuj Kumar

We propose a new convex integration scheme in fluid mechanics, and we provide an application to the two-dimensional Euler equations. We prove the flexibility and nonuniqueness of $…

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.AP2024

Sharp Nonuniqueness in the Transport Equation with Sobolev Velocity Field

Elia Bruè, Maria Colombo, Anuj Kumar

Given a divergence-free vector field $u \in L_{t}^{\infty} W_{x}^{1, p} (R^{d})$ and a nonnegative initial datum $ρ_{0} \in L^{r}$ , the celebrated DiPerna--Lions theory established…

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★ 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.AP2022

Onsager critical solutions of the forced Navier-Stokes equations

Elia Bruè, Maria Colombo, Gianluca Crippa +2

We answer positively to [BDL22, Question 2.4] by building new examples of solutions to the forced 3d-Navier-Stokes equations with vanishing viscosity, which exhibit anomalous dissi…

math.AP2022

Enhanced dissipation for two-dimensional Hamiltonian flows

Elia Bruè, Michele Coti Zelati, Elio Marconi

Let $H \in C^{1} \cap W^{2, p}$ be an autonomous, non-constant Hamiltonian on a compact $2$ -dimensional manifold, generating an incompressible velocity field $b = \nabla^{⊥} H$ . We give…

math.AP2022★ 1 cited

Gluing non-unique Navier-Stokes solutions

Dallas Albritton, Elia Bruè, Maria Colombo

We construct non-unique Leray solutions of the forced Navier-Stokes equations in bounded domains via gluing methods. This demonstrates a certain locality and robustness of the non-…

math.AP2022★ 32 cited

Anomalous dissipation for the forced 3D Navier-Stokes equations

Elia Bruè, Camillo De Lellis

In this paper, we consider the forced incompressible Navier-Stokes equations with vanishing viscosity on the three-dimensional torus. We show that there are (classical) solutions f…

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.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.MG2021

BV Functions and Sets of Finite Perimeter on Configuration Spaces

Elia Bruè, Kohei Suzuki

This paper contributes to foundations of the geometric measure theory in the infinite dimensional setting of the configuration space over the Euclidean space $R^{n}$ equipped…

math.DG2021★ 30 cited

On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth

Gioacchino Antonelli, Elia Bruè, Mattia Fogagnolo +1

In this paper we provide new existence results for isoperimetric sets of large volume in Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth. We find…

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★ 34 cited

A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics II

Elia Bruè, Mattia Calzi, Giovanni E. Comi +1

We continue the study of the space $B V^{α} (R^{n})$ of functions with bounded fractional variation in $R^{n}$ and of the distributional fractional Sobolev space $S^{α,p}(\…

math.AP2020★ 19 cited

Advection diffusion equations with Sobolev velocity field

Elia Bruè, Quoc-Hung Nguyen

In this note we study advection diffusion equations associated to incompressible $W^{1, p}$ velocity fields with $p > 2$ . We present new estimates on the energy dissipation rate and w…

math.AP2020★ 51 cited

Positive solutions of transport equations and classical nonuniqueness of characteristic curves

Elia Bruè, Maria Colombo, Camillo De Lellis

The seminal work of DiPerna and Lions [Invent. Math., 98, 1989] guarantees the existence and uniqueness of regular Lagrangian flows for Sobolev vector fields. The latter is a suita…

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…

Ollivier--Ricci Curvature on Groups of Polynomial Growth

Fukaya-Yamaguchi Conjecture in Dimension Four

Compact Manifolds with Unbounded Nilpotent Fundamental Groups and Positive Ricci Curvature

Lower Ricci Curvature Bounds and the Orientability of Spaces

Flexibility of Two-Dimensional Euler Flows with Integrable Vorticity

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

Sharp Nonuniqueness in the Transport Equation with Sobolev Velocity Field

Six dimensional counterexample to the Milnor Conjecture

Stability of Tori under Lower Sectional Curvature

Fundamental Groups and the Milnor Conjecture

Onsager critical solutions of the forced Navier-Stokes equations

Enhanced dissipation for two-dimensional Hamiltonian flows

Gluing non-unique Navier-Stokes solutions

Anomalous dissipation for the forced 3D Navier-Stokes equations

The metric measure boundary of spaces with Ricci curvature bounded below

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

BV Functions and Sets of Finite Perimeter on Configuration Spaces

On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth

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

Boundary regularity and stability for spaces with Ricci bounded below

A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics II

Advection diffusion equations with Sobolev velocity field

Positive solutions of transport equations and classical nonuniqueness of characteristic curves

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

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

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