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Relative Symplectic Caps, Fibered Knots And 4-Genus
(2014-04-07)
The 4-genus of a knot in S3 is an important measure of complexity, related to the unknotting number. A fundamental result used to study the 4-genus and related invariants of homology classes is the Thom conjecture, proved ...
Infinitely Divisible Metrics, Curvature Inequalities And Curvature Formulae
(2014-06-30)
The curvature of a contraction T in the Cowen-Douglas class is bounded above by the
curvature of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. ...
Function Theory On Non-Compact Riemann Surfaces
(2014-06-30)
The theory of Riemann surfaces is quite old, consequently it is well developed. Riemann surfaces originated in complex analysis as a means of dealing with the problem of multi-valued functions. Such multi-valued functions ...
Ricci Flow And Isotropic Curvature
(2014-09-03)
This thesis consists of two parts. In the first part, we study certain Ricci flow invariant nonnegative curvature conditions as given by B. Wilking. We begin by proving that any such nonnegative curvature implies nonnegative ...