Heat Kernel Approximation on Kendall Shape Space

2020 ◽  
Author(s):  
Riadh Mtibaa ◽  
Salam Khan
Keyword(s):  
Closed Form ◽  
Heat Kernel ◽  
Shape Space ◽  
Beltrami Operator ◽  
Heat Kernel Expansion ◽  
Kernel Approximation ◽  
Recursion Scheme ◽  
Recursion Formulas ◽  
Angular Coordinates

The heat kernel on Kendall shape subspaces is approximated by an expansion. The Kendall space is useful for representing the shapes associated to collections of landmarks’positions. The Minakshisundaram-Pleijel recursion formulas are used in order to calculate the closed-form approximations of the first and second coefficients of the heat kernel expansion. Prior to the exploitation of the recursion scheme, the expression of the Laplace-Beltrami operator is adapted to the targeted space using geodesic spherical and angular coordinates.

scholarly journals Logarithmic correction to the entropy of extremal black holes in $$ \mathcal{N} $$ = 1 Einstein-Maxwell supergravity

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Gourav Banerjee ◽  
Sudip Karan ◽  
Binata Panda
Keyword(s):  
Black Holes ◽  
Heat Kernel ◽  
Proper Time ◽  
Logarithmic Correction ◽  
Functional Determinant ◽  
Supergravity Theory ◽  
Heat Kernel Expansion ◽  
Determinant Of Laplacian ◽  
Extremal Black Holes ◽  
Classical Background

Abstract We study one-loop covariant effective action of “non-minimally coupled” $$ \mathcal{N} $$ N = 1, d = 4 Einstein-Maxwell supergravity theory by heat kernel tool. By fluctuating the fields around the classical background, we study the functional determinant of Laplacian differential operator following Seeley-DeWitt technique of heat kernel expansion in proper time. We then compute the Seeley-DeWitt coefficients obtained through the expansion. A particular Seeley-DeWitt coefficient is used for determining the logarithmic correction to Bekenstein-Hawking entropy of extremal black holes using quantum entropy function formalism. We thus determine the logarithmic correction to the entropy of Kerr-Newman, Kerr and Reissner-Nordström black holes in “non-minimally coupled” $$ \mathcal{N} $$ N = 1, d = 4 Einstein-Maxwell supergravity theory.

scholarly journals The Polyakov loop and the heat kernel expansion at finite temperature

2003 ◽  
Vol 563 (3-4) ◽  
pp. 173-178 ◽  
Author(s):  
E. Megı́as ◽  
E. Ruiz Arriola ◽  
L.L. Salcedo
Keyword(s):  
Heat Kernel ◽  
Finite Temperature ◽  
Polyakov Loop ◽  
Heat Kernel Expansion

The Heat Kernel and Green's Function on a Manifold with Heisenberg Group as Boundary

2004 ◽  
Vol 56 (3) ◽  
pp. 590-611
Author(s):  
Yilong Ni
Keyword(s):  
Riemannian Manifold ◽  
Heisenberg Group ◽  
Green’S Function ◽  
Heat Kernel ◽  
Green's Function ◽  
Beltrami Operator ◽  
Small Time ◽  
Time Estimates

AbstractWe study the Riemannian Laplace-Beltrami operator L on a Riemannian manifold with Heisenberg group H1 as boundary. We calculate the heat kernel and Green's function for L, and give global and small time estimates of the heat kernel. A class of hypersurfaces in this manifold can be regarded as approximations of H1. We also restrict L to each hypersurface and calculate the corresponding heat kernel and Green's function. We will see that the heat kernel and Green's function converge to the heat kernel and Green's function on the boundary.

Heat kernel expansion on a generalized cone

1989 ◽  
Vol 30 (4) ◽  
pp. 770-773 ◽  
Author(s):  
J. S. Dowker
Keyword(s):  
Heat Kernel ◽  
Heat Kernel Expansion

Heat kernel expansion in geometric fields

1987 ◽  
Vol 195 (3) ◽  
pp. 435-438 ◽  
Author(s):  
Guido Cognola ◽  
Sergio Zerbini
Keyword(s):  
Heat Kernel ◽  
Heat Kernel Expansion
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