Daniele Valtorta

Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound

We complete the picture of sharp eigenvalue estimates for the

Volume Estimates on the Critical Sets of Solutions to Elliptic PDEs

p

Critical sets of elliptic equations

p-Laplacian on a compact manifold by providing sharp estimates on the first nonzero eigenvalue of the nonlinear operator

Quantitative regularity for p-harmonic maps

\Delta _p

Stokes' theorem, volume growth and parabolicity

Δp when the Ricci curvature is bounded from below by a negative constant. We assume that the boundary of the manifold is convex, and put Neumann boundary conditions on it. The proof is based on a refined gradient comparison technique and a careful analysis of the underlying model spaces.

Rectifiability and upper Minkowski bounds for singularities of harmonic Q-valued maps

In this paper we study the regularity of stationary and minimizing harmonic maps