Curvature varifolds with orthogonal boundary
Abstract: We consider the class
of -dimensional surfaces in
that intersect orthogonally along the boundary. A piece of an affine -plane in
is called an orthogonal slice. We prove estimates for the area by the integral of the second fundamental form in three cases: first, when admits no orthogonal slices, second for if all orthogonal slices are topological disks, and finally, for all if the surfaces are confined to a neighborhood of . The orthogonality constraint has a weak formulation for curvature varifolds. We classify those varifolds of vanishing curvature. As an application, we prove for any the existence of an orthogonal 2-varifold that minimizes the curvature in the integer rectifiable class
- Location
-
Deutsche Nationalbibliothek Frankfurt am Main
- Extent
-
Online-Ressource
- Language
-
Englisch
- Notes
-
Journal of the London Mathematical Society. - 110, 3 (2024) , e12976, ISSN: 1469-7750
- Event
-
Veröffentlichung
- (where)
-
Freiburg
- (who)
-
Universität
- (when)
-
2024
- Creator
- DOI
-
10.1112/jlms.12976
- URN
-
urn:nbn:de:bsz:25-freidok-2569309
- Rights
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
-
25.03.2025, 1:48 PM CET
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Kuwert, Ernst
- Müller, Marius
- Universität
Time of origin
- 2024
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