Logo del repository
  1. Home
 
Opzioni

Existence and uniqueness of parallel transport on non-collapsed RCD(K,N) spaces

Caputo, Emanuele
2021-12-17
Abstract
The thesis mainly contains the construction of parallel transport on non-collapsed spaces, obtained in the work "Parallel transport on non-collapsed RCD(K,N)", done in collaboration with my supervisor N. Gigli and E. Pasqualetto. We obtain both existence and uniqueness results. Our theory covers the case of geodesics and, more generally, of curves obtained via the flow of sufficiently regular time dependent vector fields. In this generality, we don't study parallel transport along a single such curve, but along a generic collection of such integral curves. The notion of flow under consideration is the one of regular Lagrangian flow, after the axiomatization in the nonsmooth setting by Ambriosio and Trevisan. A preliminary introduction on calculus on metric measure spaces and the theory of flows of Sobolev vector fields, both in euclidean and nonsmooth setting, is also included.
Archivio
http://hdl.handle.net/20.500.11767/125509
Diritti
open access
Soggetti
  • Parallel transport

  • RCD space

  • Regular Lagrangian fl...

  • Metric geometry

  • Geometric analysis

  • Settore MAT/05 - Anal...

google-scholar
Get Involved!
  • Source Code
  • Documentation
  • Slack Channel
Make it your own

DSpace-CRIS can be extensively configured to meet your needs. Decide which information need to be collected and available with fine-grained security. Start updating the theme to match your nstitution's web identity.

Need professional help?

The original creators of DSpace-CRIS at 4Science can take your project to the next level, get in touch!

Realizzato con Software DSpace-CRIS - Estensione mantenuta e ottimizzata da 4Science

  • Impostazioni dei cookie
  • Informativa sulla privacy
  • Accordo con l'utente finale
  • Invia il tuo Feedback