Lecture Notes on Mean Curvature Flow, Barriers and Singular Perturbations
The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are descri...
| Κύριος συγγραφέας: | |
|---|---|
| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Pisa :
Scuola Normale Superiore : Imprint: Edizioni della Normale,
2013.
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| Σειρά: | Publications of the Scuola Normale Superiore ;
12 |
| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- Signed distance from a smooth boundary
- Mean curvature vector and second fundamental form
- First variations of volume integrals and of the perimeter
- Smooth mean curvature flows
- Huisken’s monotonicity formula
- Inclusion principle. Local well posedness: the approach of Evans–Spruck
- Grayson’s example
- De Giorgi’s barriers
- Inner and outer regularizations
- An example of fattening
- Ilmanen’s interposition lemma
- The avoidance principle
- Comparison between barriers and a generalized evolution
- Barriers and level set evolution
- Parabolic singular perturbations: formal matched asymptotics, convergence and error estimate.
