New and old sub-Riemannian challenges bridging analysis and geometry

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.

Grantor dc:publisher

Università degli studi di Trento

Year dc:date

2024

Author dc:creator

• Verzellesi, Simone

Contributors dc:contributor

• Pinamonti, Andrea

• sub-Riemannian geometry, Heisenberg group, minimal surfaces, viscosity solutions, integral representation, Bernstein problem, prescribed mean curvature.
• Settore MAT/05 - Analisi Matematica
• Settore MATH-03/A - Analisi matematica

Statement dc:rights

• info:eu-repo/semantics/openAccess
• license:Creative commons
• license uri:http://creativecommons.org/licenses/by-nc-sa/4.0/

Language dc:language

eng

Identifier

http://dx.doi.org/10.15168/11572_437934
10.15168/11572_437934

OAI identifier oai:identifier

oai:iris.unitn.it:11572/437934