A Priori Estimates for the Homogeneous Monge-Ampère Equation on Kähler Manifolds

Brubaker, Katherine Ann

doi:10.25394/PGS.9730208.v1

KBrubaker thesis.pdf (407.23 kB)

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A Priori Estimates for the Homogeneous Monge-Ampère Equation on Kähler Manifolds

thesis

posted on 2019-10-16, 18:48 authored by Katherine Ann BrubakerKatherine Ann Brubaker

This thesis investigates the existence of smooth solutions to MA(F), proving a priori estimates on the leaves of the foliation that corresponds to smooth solutions. We demonstrate that sequences of leaves of Monge-Amp`ere foliations converge to holomorphic disks.

History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

West Lafayette

Advisor/Supervisor/Committee Chair

Laszlo Lempert

Additional Committee Member 2

Sai-Kee Yeung

Additional Committee Member 3

Steven R. Bell

Additional Committee Member 4

Chi Li

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Keywords

complex geometry several complex variables Non-linear partial differential equations foliation Kahler manifolds space of Kahler metrics Monge-Ampere equation Pure Mathematics not elsewhere classified Mathematical Sciences not elsewhere classified

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CC BY 4.0

A Priori Estimates for the Homogeneous Monge-Ampère Equation on Kähler Manifolds

History

Degree Type

Department

Campus location

Advisor/Supervisor/Committee Chair

Additional Committee Member 2

Additional Committee Member 3

Additional Committee Member 4

Usage metrics

Categories

Keywords

Licence

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