This thesis consists of two parts: In part I we apply the statistical mechanics techniques to a generalization of the prescribed $Q$-curvature problem, especially on the $mbox{sc d}$-dim sphere $mathbb S^{smallmbox{sc d}}$. We introduce a coupling constant $c$ on top of the configurational canonical ensemble and study the weak convergence of this new canonical ensemble. In this part, the $Q$-curvature does not change sign. In part II the statistical mechanics technique is generalized to the prescribed $Q$-curvature problem with sign-change, while the mechanical interpretation will be lost. We decompose a single differential equation into a system of two differential equations, and the statistical mechanics technique can be applied to each equation.
Subject (authority = RUETD)
Topic
Mathematics
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_4734
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
vi, 78 p. : ill.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = vita)
Includes vita
Note (type = statement of responsibility)
by Yu Wang
Subject (authority = ETD-LCSH)
Topic
Curvature
Subject (authority = ETD-LCSH)
Topic
Mathematical statistics
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
Rutgers University. Graduate School - New Brunswick
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License
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Author Agreement License
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