The Anisotropic Gaussian Isoperimetric Inequality and Ehrhard Symmetrization

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dc.contributor.advisorToro, Tatiana
dc.contributor.authorYeh, Kuan-Ting
dc.date.accessioned2024-09-09T23:12:42Z
dc.date.issued2024-09-09
dc.date.submitted2024
dc.descriptionThesis (Ph.D.)--University of Washington, 2024
dc.description.abstractIn this thesis, we establish the isoperimetric inequality for the anisotropic Gaussian measure and characterize the cases of equality. Additionally, we present an example demonstrating that Ehrhard symmetrization fails to decrease for the anisotropic Gaussian perimeter and introduce a new inequality that includes an error term. This new inequality, in particular, provides a clue to a uniqueness result for the Ehrhard measure within the class of anisotropic Gaussian measures. Our final result, a collaboration with Sean McCurdy, expands the class of measures to which the previous uniqueness result applies.
dc.embargo.lift2025-09-09T23:12:42Z
dc.embargo.termsRestrict to UW for 1 year -- then make Open Access
dc.format.mimetypeapplication/pdf
dc.identifier.otherYeh_washington_0250E_26818.pdf
dc.identifier.urihttps://hdl.handle.net/1773/52106
dc.language.isoen_US
dc.rightsCC BY
dc.subjectAnisotropic Gaussian Isoperimetric Inequality
dc.subjectAnisotropic Gaussian Measures
dc.subjectEhrhard Symmetrization
dc.subjectGaussian Isoperimetric Inequality
dc.subjectIsoperimetric Inequality
dc.subjectMathematics
dc.subject.otherMathematics
dc.titleThe Anisotropic Gaussian Isoperimetric Inequality and Ehrhard Symmetrization
dc.typeThesis

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