90 citations · 365 across the 17 of their papers we have counts for
10 papers · 1 filter
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…
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 $…
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…