The aim of this thesis is to propose a systematic exposition of some analytic and geometric problems arising from the study of sub-Riemannian geometry, Carnot-Carathéodory spaces and, more broadly, anisotropic metric and differential structures. We deal with four main topics. 1 Calculus of variations for local functionals depending on vector fields 2 PDEs over Carnot-Carathéodory structures. 3 Regularity theory for almost perimeter minimizers in Carnot groups. 4 Geometry of hypersurfaces in Heisenberg groups.

New and old sub-Riemannian challenges bridging analysis and geometry / Verzellesi, Simone. - (2024 Nov 15), pp. 1-394. [10.15168/11572_437934]

New and old sub-Riemannian challenges bridging analysis and geometry

Verzellesi, Simone
2024-11-15

Abstract

The aim of this thesis is to propose a systematic exposition of some analytic and geometric problems arising from the study of sub-Riemannian geometry, Carnot-Carathéodory spaces and, more broadly, anisotropic metric and differential structures. We deal with four main topics. 1 Calculus of variations for local functionals depending on vector fields 2 PDEs over Carnot-Carathéodory structures. 3 Regularity theory for almost perimeter minimizers in Carnot groups. 4 Geometry of hypersurfaces in Heisenberg groups.
15-nov-2024
XXXVII
2023-2024
Matematica (29/10/12-)
Mathematics
Pinamonti, Andrea
no
Inglese
Settore MAT/05 - Analisi Matematica
Settore MATH-03/A - Analisi matematica
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