552 citations · 2k across the 45 of their papers we have counts for
4 papers · 1 filter
A first-order condition for the independence on of weak gradients
Nicola Gigli, Francesco Nobili
It is well known that on arbitrary metric measure spaces, the notion of minimal -weak upper gradient may depend on . In this paper we investigate how a first-order condition…
Weakly non-collapsed RCD spaces are strongly non-collapsed
Camillo Brena, Nicola Gigli, Shouhei Honda +1
We prove that any weakly non-collapsed RCD space is actually non-collapsed, up to a renormalization of the measure. This confirms a conjecture raised by De Philippis and the second…
Parallel transport on non-collapsed spaces
Emanuele Caputo, Nicola Gigli, Enrico Pasqualetto
We provide a general theory for parallel transport on non-collapsed spaces obtaining both existence and uniqueness results. Our theory covers the case of geodesics and,…
Monotonicity formulas for harmonic functions in spaces
Nicola Gigli, Ivan Yuri Violo
We generalize to the setting a family of monotonicity formulas by Colding and Minicozzi for positive harmonic functions in Riemannian manifolds with non-negative R…