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Steiner symmetrization and the eigenvalues of the Laplace operator on polygons
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Weightman, Ryan. Steiner symmetrization and the eigenvalues of the Laplace operator on polygons. Retrieved from https://doi.org/doi:10.7282/t3-kv4y-c720

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TitleSteiner symmetrization and the eigenvalues of the Laplace operator on polygons
NameWeightman, Ryan (author); Fu, Siqi (chair); Rutgers University; Camden Graduate School
Date Created2021
Other Date2021-05 (degree)
SubjectSteiner symmetrization, Mathematics
Extent1 online resource (iv, 59 pages)
DescriptionThe topic that I chose to explore for this thesis is a study of the eigenvalues of the Dirichlet Laplacian on a two dimensional domain and the properties that arise as a direct consequence to them. The eigenvalues of a given domain pro- duce so many surprising insights that simply the study of a triangular domain has many directions in which one could explore. What I love about this topic is that throughout my study, a resource from 1966 could take me to a resource from the 1700’s which could lead me all the way back to 2013. It is a topic rich with exploration, both new and old which really gave me a good picture of what modern research in pure mathematics can look like.

The goal with this thesis was simple; understand a few of the implications brought up by the famous question of Mark Kac, “Can one hear the shape of a drum?” and then possibly, with enough effort, make some type of original contribution to the topic.

In my study of these domains, I was inevitably brought back to the isoperimetric inequality leading me to a process called Steiner Symmetrization. This process was introduced to me by [7]. We were able to use some basic trigonom- etry to fill in the detail in the treatise of George Polya and come up with simplified proofs of special cases of such symmetrization.
NoteM.S.
NoteIncludes bibliographical references
Genretheses, ETD graduate
Persistent URLhttps://doi.org/doi:10.7282/t3-kv4y-c720
LanguageEnglish
CollectionCamden Graduate School Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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