Regularity problems in sub-Riemannian structures (n. 2022F4F2LH)
Type
PRIN 2022, D.D. n. 104 del 2 febbraio 2022
CUP
C53D23002450006
Principal Investigator
Giovanna Citti (Università degli Studi di Bologna)
Other research units
UO1 - Giovanna CITTI - Università degli Studi di BOLOGNA
UO2 - Roberto MONTI - Università degli Studi di PADOVA
UO3 - Francesco SERRA CASSANO - Università degli Studi di TRENTO
Duration
28/09/2023 - 31/12/2025
Description
This research project focused on the theory of minimal surfaces in the
Heisenberg group. One of the most important open problems in this field
is the regularity of H-minimal surfaces.
With Giacomo Vianello, postdoc financed by the Prin, we obtained results
related to the existence, structure, and regularity of solutions to the
Plateau problem in the first Heisenberg group.
The setting is the one of intrinsic graphs defined on a convex domain D
of a vertical plane. The theory holds depending on a smallness
condition either on the boundary of D or on the boundary datum phi. The
core of the proof relies on a calibration argument.
The techniques can be used to establish new regularity results for
H-perimeter minimizers.
