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.File | Dimensione | Formato | |
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PhD_Thesis_VERZELLESI_22_10_24.pdf
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Tesi di dottorato (Doctoral Thesis)
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