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Now showing items 1-9 of 9

#### On an ODE Associated to the Ricci Flow

(2018-04-18)

We discuss two topics in this talk. First we study compact Ricci-flat four dimensional manifolds without boundary and obtain point wise restrictions on curvature( not involving global quantities such as volume and diameter) ...

#### On the Stability of Certain Riemannian Functionals

(2018-03-06)

Given a compact smooth manifold Mn without boundary and n ≥ 3, the Lp-norm of the curvature tensor,
defines a Riemannian functional on the space of Riemannian metrics with unit volume M1. Consider ...

#### 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 ...

#### An Introduction to Minimal Surfaces

(2017-12-10)

In the first chapter of this report, our aim is to introduce harmonic maps between Riemann surfaces using the Energy integral of a map. Once we have the desired prerequisites, we move on to show how to continuously deform ...

#### 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 ...

#### Numerical Study Of Regularization Methods For Elliptic Cauchy Problems

(2011-06-30)

Cauchy problems for elliptic partial differential equations arise in many important applications, such as, cardiography, nondestructive testing, heat transfer, sonic boom produced by a maneuvering aerofoil, etc. Elliptic ...

#### Riemann Roch Theorem For Algebraic Curves

(2011-09-28)