90 citations · 365 across the 17 of their papers we have counts for
21 papers
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…
Quantitative Reifenberg theorem for measures
Nick Edelen, Aaron Naber, Daniele Valtorta
We study generalizations of Reifenberg's Theorem for measures in under assumptions on the Jones' -numbers, which appropriately measure how close the support is to…
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…
Stratification for the singular set of approximate harmonic maps
Aaron Naber, Daniele Valtorta
The aim of this note is to extend the results in arXiv:1504.02043 to the case of approximate harmonic maps. More precisely, we will proved that the singular strata of an a…
Energy Identity for Stationary Yang Mills
A. Naber, D. Valtorta
Given a principal bundle over a Riemannian manifold with compact structure group , let us consider a stationary Yang-Mills connection with energy $\int_M |F_A|^2\le…
The Singular Structure and Regularity of Stationary and Minimizing Varifolds
Aaron Naber, Daniele Valtorta
If one considers an integral varifold with bounded mean curvature, and if $S^k(I)\equiv\{x\in M: \text{ no tangent cone at $x$ is }k+1\text{-symmetric}\}$ is the s…
Rectifiable-Reifenberg and the Regularity of Stationary and Minimizing Harmonic Maps
Aaron Naber, Daniele Valtorta
In this paper we study the regularity of stationary and minimizing harmonic maps between Riemannian manifolds. If $S^k(f)\equiv\{x\in M: \text{ no tangen…
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 p-Laplace operator on Riemannian manifolds
Daniele Valtorta
This thesis covers different aspects of the p-Laplace operators on Riemannian manifolds. Chapter 2. Potential theoretic aspects: the Khasmkinskii condition. Chapter 3: sharp eigenv…
Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound
Aaron Naber, Daniele Valtorta
We complete the picture of sharp eigenvalue estimates for the p-Laplacian on a compact manifold by providing sharp estimates on the first nonzero eigenvalue of the nonlinear operat…
Critical sets of elliptic equations
Jeff Cheeger, Aaron Naber, Daniele Valtorta
Given a solution to a linear homogeneous second order elliptic equation with Lipschitz coefficients, we introduce techniques for giving improved estimates of the critical set $…
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…
Sharp estimate on the first eigenvalue of the p-Laplacian on compact manifold with nonnegative Ricci curvature
Daniele Valtorta
We prove the sharp estimate on the first nonzero eigenvalue of the p-laplacian on a compact Riemannian manifold with nonnegative Ricci curvature and possibly with convex boundary (…
Reverse Khas'minskii condition
Daniele Valtorta
The aim of this paper is to present and discuss some equivalent characterizations of p-parabolicity in terms of existence of special exhaustion functions. In particular, Khas'minsk…
Stokes' theorem, volume growth and parabolicity
Daniele Valtorta, Giona Veronelli
We present some new Stokes' type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Ne…
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…