dc.contributor.author Minter, Paul dc.date.accessioned 2022-06-29T16:36:36Z dc.date.available 2022-06-29T16:36:36Z dc.date.submitted 2022-04-01 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/338422 dc.description.abstract We study the structure of large classes of stable codimension one stationary integral varifolds $V$ near higher multiplicity hyperplanes and classical cones, i.e. cones supported on half-hyperplanes which have a common boundary. A key motivation for our work is to understand the local structure of stationary integral varifolds about their branch points. In addition to the hypotheses above, the only additional assumption we make is that the varifolds do not admit classical singularities of certain densities. More precisely, for any given $Q\in \{3/2,2,5/2,3,\dotsc\}$ we consider the class $\mathcal{S}_Q$ of codimension one stationary integral varifolds which have stable regular part and admit no classical singularities of density $1$ when branch points are present in the nearby varifold, and in particular completes the analysis of the singular set of $V\in\mathcal{S}_2$ in the region where the density is $<3$, up to a set of dimension at most $n-2$. dc.description.sponsorship UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L016516/1 dc.rights All Rights Reserved dc.rights.uri https://www.rioxx.net/licenses/all-rights-reserved/ dc.subject Minimal Surfaces dc.subject Branch Point dc.subject Calculus of Variations dc.subject Regularity dc.subject Geometric Measure Theory dc.title On the Structure and Regularity of Stable Branched Minimal Hypersurfaces dc.type Thesis dc.type.qualificationlevel Doctoral dc.type.qualificationname Doctor of Philosophy (PhD) dc.publisher.institution University of Cambridge dc.date.updated 2022-06-24T12:58:40Z dc.identifier.doi 10.17863/CAM.85835 rioxxterms.licenseref.uri https://www.rioxx.net/licenses/all-rights-reserved/ rioxxterms.type Thesis pubs.funder-project-id EPSRC (2334231) cam.supervisor Wickramasekera, Neshan cam.depositDate 2022-06-24 pubs.licence-identifier apollo-deposit-licence-2-1 pubs.licence-display-name Apollo Repository Deposit Licence Agreement
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