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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01cf95jf84p
Title: Interior regularity for area-minimizing currents
Authors: Skorobogatova, Anna
Advisors: De Lellis, Camillo
Contributors: Mathematics Department
Subjects: Mathematics
Issue Date: 2024
Publisher: Princeton, NJ : Princeton University
Abstract: In this thesis, we study the interior regularity of area-minimizing integral currents and codimension 1 mod(p) area-minimizing currents. For m-dimensional area-minimizing integral currents of arbitrary codimension, we strengthen Almgren’s celebrated sharp Hausdorff dimension estimate of m−2 for the singular set, first improving it to a local upper Minkowski dimension estimate of m−2. We then further demonstrate that the singular set is in fact (m−2)-rectifiable and the tangent cone is unique at H^{m−2}-a.e. point. The latter is based on a series of joint works with Camillo De Lellis and Paul Minter.For m-dimensional area-minimizing mod(p) currents of codimension 1, we demonstrate (m−2)-rectifiability of the interior singularities with flat tangent cones. In combination with works of Naber-Valtorta, Minter-Wickramasekera and De Lellis-Hirsch-Marchese-Spoloar-Stuvard, this provides a detailed structural characterization of the interior singular set in this setting.
URI: http://arks.princeton.edu/ark:/88435/dsp01cf95jf84p
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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