- Variations for submanifolds of fixed degree
- Giovannardi, Gianmarco <1992>
Subject
- MAT/05 Analisi matematica
Description
- The aim of this PhD thesis is to study the area functional for submanifolds immersed in an equiregular graded manifold. This setting, extends the sub-Riemannian one, removing the bracket generating condition. However, even in the sub-Riemannian setting only sub-manifolds of dimension or codimension one have been extensively studied. We will study the general case and observe that in higher codimension new phenomena arise, which can not show up in the Riemannian case. In particular, we will prove the existence of isolated surfaces, which do not admit degree preserving variation: a phenomena observed by now only for curves, related to the notion of abnormal geodesics.
Date
- 2020-06-18
Type
- Doctoral Thesis
- PeerReviewed
Format
- application/pdf
Identifier
urn:nbn:it:unibo-26114
Giovannardi, Gianmarco (2020) Variations for submanifolds of fixed degree, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica