Convergence of complete Ricci-βat manifolds
Name
1191267704-MIT.pdf
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697.34 KB
Format
Adobe PDF
Checksum (MD5)
099be4da6cc840753c1436f75742afea
Author(s)
Park, Jiewon.
Advisor(s)
Tobias Holck Colding.
Date Issued
2020
Publisher
Massachusetts Institute of Technology
Abstract
This thesis is focused on the convergence at inαnity of complete Ricci βat manifolds. In the αrst part of this thesis, we will give a natural way to identify between two scales, potentially arbitrarily far apart, in the case when a tangent cone at inαnity has smooth cross section. The identiαcation map is given as the gradient βow of a solution to an elliptic equation. We use an estimate of Colding-Minicozzi of a functional that measures the distance to the tangent cone. In the second part of this thesis, we prove a matrix Harnack inequality for the Laplace equation on manifolds with suitable curvature and volume growth assumptions, which is a pointwise estimate for the integrand of the aforementioned functional. This result provides an elliptic analogue of matrix Harnack inequalities for the heat equation or geometric βows.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 57-59).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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