The specific form of the constant term in the asymptotic expansion of the heat-kernel on an axially-symmetric space with a codimension two fixed-point set of conical singularities is used to determine the conformal change of the effective action in four dimensions. Another

of the Dissertation Gluing Techniques in Calibrated Geometry by Yongsheng Zhang Doctor of Philosophy in Mathematics Stony Brook University 2013 This thesis is concerned with the question: given a submanifold (perhaps with singularities), when is it possible to change the metric in some specific way so that the submanifold becomes homologically mass-minimizing? We studied this question for “hori...

We study the conformal window of asymptotically free gauge theories containing ${N}_{f}$ flavors fermion matter transforming to vector and two-index representations $SO(N),SU(N)$ $Sp(2N)$ groups. For $SO(N)$ we also consider spinorial representation. determine critical number ${N}_{f}^{\mathrm{cr}}$, corresponding lower end window, by using conjectured condition on anomalous dimension bilinear ...

We study the consequences of timelike and spaccelike conformal Ricci and conformal matter collineations for anisotropic fluid in the context of General Relativity. Necessary and sufficient conditions are derived for a spacetime with anisotropic fluid to admit conformal Ricci and conformal matter collineations parallel to u and x. These conditions for timelike and spacelike conformal Ricci and c...

using the electrostatic capacity of a condenser, the existence of a distance function on a finsler space is discussed. this distance function divides finsler spaces into the two classes, denoted here by i and ii. the topology generated by this distance on the finsler spaces of class ii coincides with its intrinsic topology. this work provides a natural extension of mathematical analysis tools n...

Many medical imaging applications require the computation of dense correspondence vector fields that match one surface with another. Surface-based registration is useful for tracking brain change, registering functional imaging data from multiple subjects, and for creating statistical shape models of anatomy. To avoid the need for a large set of manually-defined landmarks to constrain these sur...

Abstract. The aim of this work is to develop a systematic manner to close overdetermined systems arising from conformal Killing tensors (CKT). The research performs this action for 1-tensor and 2-tensors. This research makes it possible to develop a new general method for any rank of CKT. This method can also be applied to other types of Killing equations, as well as to overdetermined systems c...

We consider the problem of constructing quasi-conformal mappings between surfaces by solving Beltrami equations. This is of great importance for shape registration. In the physical world, most surface deformations can be rigorously modeled as quasi-conformal maps. The local deformation is characterized by a complex-value function, Beltrami coefficient, which describes the deviation from conform...