90 citations · 365 across the 17 of their papers we have counts for
10 papers · 1 filter
Rectifiable Reifenberg and uniform positivity under almost calibrations
Nicholas Edelen, Aaron Naber, Daniele Valtorta
The Reifenberg theorem \cite{reif_orig} tells us that if a set is uniformly close on all points and scales to a -dimensional subspace, then…
Energy Identity for Stationary Harmonic Maps
Aaron Naber, Daniele Valtorta
In this paper we consider sequences of stationary harmonic maps between smooth Riemannian manifolds with uniformly bounded energy $E[u_j]\equiv \int |\nab…
Approximation, regularity and positivity preservation on Riemannian manifolds
Stefano Pigola, Daniele Valtorta, Giona Veronelli
The paper focuses on the -Positivity Preservation property (-PP for short) on a Riemannian manifold . It states that any function with ,…
Effective Reifenberg theorems in Hilbert and Banach spaces
Nicholas Edelen, Aaron Naber, Daniele Valtorta
The aim of this article is to study effective Reifenberg theorems for measures in a Hilbert or Banach space. For Hilbert spaces, we see all the results from continue…
Rectifiability of the singular set of multiple valued energy minimizing harmonic maps
Jonas Hirsch, Salvatore Stuvard, Daniele Valtorta
In this paper we study the singular set of Dirichlet-minimizing -valued maps from into a smooth compact manifold without boundary. Similarly to what…
Rectifiability and upper Minkowski bounds for singularities of harmonic Q-valued maps
Camillo de Lellis, Andrea Marchese, Emanuele Spadaro +1
In this article we prove that the singular set of Dirichlet-minimizing -valued functions is countably -rectifiable and we give upper bounds for the -dimensional Mi…
Quantitative regularity for p-harmonic maps
Aaron Naber, Daniele Valtorta, Giona Veronelli
In this article, we study the regularity of minimizing and stationary -harmonic maps between Riemannian manifolds. The aim is obtaining Minkowski-type volume estimates on the si…
Volume estimates on the critical sets of solutions to elliptic PDEs
Aaron Naber, Daniele Valtorta
In this paper we study solutions to elliptic linear equations , either on or a Riemannian manifold, u…
On the equivalence of stochastic completeness, Liouville and Khas'minskii condition in linear and nonlinear setting
Luciano Mari, Daniele Valtorta
Set in Riemannian enviroment, the aim of this paper is to present and discuss some equivalent characterizations of the Liouville property relative to special operators, in some sen…
Generalized external cone condition for domains in Riemannian manifolds
Daniele Valtorta
The aim of this note is to present an alternative proof for an already known result relative to the solvability of the Dirichlet problem in Riemannian manifolds (see remark 0.1). I…