Bruno Franchi

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math.AP2024

Primitives of volume forms in Carnot groups

Annalisa Baldi, Bruno Franchi, Pierre Pansu

In the Euclidean space it is known that a function $f \in L^{2}$ of a ball, with vanishing average,is the divergence of a vector field $F \in L^{2}$ with$$\| F\|\_{ L^2(B)} \le C \|f\|\_…

math.AP2024

Continuous primitives for higher degree differential forms in Euclidean spaces, Heisenberg groups and applications

Annalisa Baldi, Bruno Franchi, Pierre Pansu

It is shown that higher degree exact differential forms on compact Riemannian $n$ -manifolds possess continuous primitives whose uniform norm is controlled by their $L^{n}$ norm. A co…