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Partial differential equations and v...

Rubin, Daniel.

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Partial differential equations and variational approaches to constant scalar curvature metrics in Kahler geometry.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Partial differential equations and variational approaches to constant scalar curvature metrics in Kahler geometry./
作者:	Rubin, Daniel.
面頁冊數:	63 p.
附註:	Source: Dissertation Abstracts International, Volume: 76-09(E), Section: B.
Contained By:	Dissertation Abstracts International76-09B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3689693
ISBN:	9781321692815

Partial differential equations and variational approaches to constant scalar curvature metrics in Kahler geometry.
Rubin, Daniel.

Partial differential equations and variational approaches to constant scalar curvature metrics in Kahler geometry. - 63 p.

Source: Dissertation Abstracts International, Volume: 76-09(E), Section: B.

Thesis (Ph.D.)--Columbia University, 2015.

In this thesis we investigate two approaches to the problem of existence of metrics of constant scalar curvature in a fixed \kahler class. In the first part, we examine the equation for constant scalar curvature under the assumption of toric symmetry, thus reducing the problem to a fourth order nonlinear degenerate elliptic equation for a convex function defined in a polytope in R n. We obtain partial results on this equation using an associated Monge-Ampere equation to determine the boundary behavior of the solution. In the second part, we consider the asymptotics of certain energy functionals and their relation to stability and the existence of minimizers. We derive explicit formulas for their asymptotic slopes, which allows one to determine whether or not (X,L) is stable, and in some cases rule out the existence of a canonical metric.

ISBN: 9781321692815Subjects--Topical Terms:

515831
Mathematics.

Partial differential equations and variational approaches to constant scalar curvature metrics in Kahler geometry.
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245 1 0 $a Partial differential equations and variational approaches to constant scalar curvature metrics in Kahler geometry.
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500 $a Adviser: Duong H. Phong.
502 $a Thesis (Ph.D.)--Columbia University, 2015.
520 $a In this thesis we investigate two approaches to the problem of existence of metrics of constant scalar curvature in a fixed \kahler class. In the first part, we examine the equation for constant scalar curvature under the assumption of toric symmetry, thus reducing the problem to a fourth order nonlinear degenerate elliptic equation for a convex function defined in a polytope in R n. We obtain partial results on this equation using an associated Monge-Ampere equation to determine the boundary behavior of the solution. In the second part, we consider the asymptotics of certain energy functionals and their relation to stability and the existence of minimizers. We derive explicit formulas for their asymptotic slopes, which allows one to determine whether or not (X,L) is stable, and in some cases rule out the existence of a canonical metric.
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