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Monotonicity for some geometric flows
Afuni, Ahmad

HaupttitelMonotonicity for some geometric flows
TitelvarianteMonotonie für einige geometrische Flüsse
AutorAfuni, Ahmad
Geburtsort: Al Ahmadi, Kuwait
GutachterProf. Dr. Klaus Ecker
weitere GutachterProf. Joseph F. Grotowski
Freie Schlagwörtergeometric evolution equations; local monotonicity; Yang-Mills flow; harmonic map heat flow; mean curvature flow
DDC510 Mathematik
ZusammenfassungThe aim of this thesis is to establish local monotonicity formulæ for solutions to Dirichlet-type flows, such as the harmonic map and Yang-Mills heat flows, and the mean curvature flow. In particular, for the former, we allow as domain an evolving Riemannian manifold and for the latter, we allow as target an evolving Riemannian manifold. The approach taken consists in first deriving divergence identities involving an appropriate evolving quantity, then integrating over superlevel sets (heat balls) of suitable kernels. A theory of heat balls analogous to that of Ecker, Knopf, Ni and Topping is developed in order to accomplish this. The main result is then that, provided certain integrals are finite, local monotonicity formulæ hold in this general setting, thus generalizing results for the mean curvature and harmonic map heat flows and establishing a new local monotonicity formula for solutions to the Yang-Mills flow.
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SeitenzahlVII, 129 S.
Fachbereich/EinrichtungFB Mathematik und Informatik
Erscheinungsjahr2015
Dokumententyp/-SammlungenDissertation
Medientyp/FormatText
SpracheEnglisch
Rechte Nutzungsbedingungen
Tag der Disputation12.01.2015
Erstellt am12.02.2015 - 13:40:18
Letzte Änderung12.02.2015 - 13:47:29
 
Statische URLhttp://edocs.fu-berlin.de/diss/receive/FUDISS_thesis_000000098567
URNurn:nbn:de:kobv:188-fudissthesis000000098567-9
Zugriffsstatistik