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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 |
Files in This Item:
File | Description | Size | Format | |
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Skorobogatova_princeton_0181D_14987.pdf | 6.68 MB | Adobe PDF | View/Download |
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