199 citations · 522 across the 42 of their papers we have counts for
4 papers · 1 filter
Non-collapsed spaces with Ricci curvature bounded from below
Guido De Philippis, Nicola Gigli
We propose a definition of non-collapsed space with Ricci curvature bounded from below and we prove the versions of Colding's volume convergence theorem and of Cheeger-Colding dime…
The injectivity radius of Lie manifolds
Paolo Antonini, Guido De Philippis, Nicola Gigli
We prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive
Existence results for minimizers of parametric elliptic functionals
Guido De Philippis, Antonio De Rosa, Francesco Ghiraldin
We prove a compactness principle for the anisotropic formulation of the Plateau problem in any codimension, in the same spirit of the previous works of the authors \cite{DelGhiMag,…
Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints
Adolfo Arroyo-Rabasa, Guido De Philippis, Filip Rindler
We show general lower semicontinuity and relaxation theorems for linear-growth integral functionals defined on vector measures that satisfy linear PDE side constraints (of arbitrar…