etd@IISc Collection:http://hdl.handle.net/2005/412014-04-24T00:12:26Z2014-04-24T00:12:26ZUncertainty Handling In Knowledge-Based Systems Via Evidence RepresentationSrinivas, Nowdurihttp://hdl.handle.net/2005/18892013-01-18T10:20:03Z2013-01-17T18:30:00ZTitle: Uncertainty Handling In Knowledge-Based Systems Via Evidence Representation
Authors: Srinivas, Nowduri2013-01-17T18:30:00ZTime Series Analysis Of Neurobiological SignalsHariharan, Nhttp://hdl.handle.net/2005/14522011-09-28T06:54:18Z2011-09-27T18:30:00ZTitle: Time Series Analysis Of Neurobiological Signals
Authors: Hariharan, N2011-09-27T18:30:00ZA Study On Solutions Of Singular Integral EquationsGeorge, A Jhttp://hdl.handle.net/2005/17362012-05-31T07:57:41Z2012-05-30T18:30:00ZTitle: A Study On Solutions Of Singular Integral Equations
Authors: George, A J2012-05-30T18:30:00ZA Study Of The Metric Induced By The Robin FunctionBorah, Digantahttp://hdl.handle.net/2005/22402013-09-13T05:25:08Z2013-09-12T18:30:00ZTitle: A Study Of The Metric Induced By The Robin Function
Authors: Borah, Diganta
Abstract: Let D be a smoothly bounded domain in Cn , n> 1. For each point p _ D, we have the Green function G(z, p) associated to the standard sum-of-squares Laplacian Δ with pole at p and the Robin constant __
Λ(p) = lim G(z, p) −|z − p−2n+2
z→p |
at p. The function p _→ Λ(p) is called the Robin function for D.
Levenberg and Yamaguchi had proved that if D is a C∞-smoothly bounded pseudoconvex domain, then the function log(−Λ) is a real analytic, strictly plurisubharmonic exhaustion function for D and thus induces a metric
ds2 = n∂2 log(−Λ)(z) dzα ⊗ dzβ
z
∂zα∂zβ
α,β=1
on D, called the Λ-metric. For an arbitrary C∞-smoothly bounded domain, they computed the boundary asymptotics of Λ and its derivatives up to order 3, in terms of a defining function for the domain. As a consequence it was shown that the Λ-metric is complete on a C∞-smoothly bounded strongly pseudoconvex domain or a C∞-smoothly bounded convex domain.
In this thesis, we study the boundary behaviour of the function Λ and its derivatives of all orders near a C2-smooth boundary point of an arbitrary domain. We compute the boundary asymptotics of the Λ-metric on a C∞-smoothly bounded pseudoconvex domain and as a consequence obtain that on a C∞-smoothly bounded strongly pseudoconvex domain, the Λ-metric is comparable to the Kobayashi metric (and hence to the Carath´eodory and the Bergman metrics). Using the boundary asymptotics of Λ and its derivatives, we calculate the holomorphic sectional curvature of the Λ-metric on a C∞-smoothly bounded strongly pseudoconvex domain at points on the inner normals and along the normal directions. The unit ball in Cn is also characterised among all C∞-smoothly bounded strongly convex domains on which the Λ-metric has constant negative holomorphic sectional curvature. Finally we study the stability of the Λ-metric under a C2 perturbation of a C∞-smoothly bounded pseudoconvex domain.
(For equation pl refer the abstract pdf file)2013-09-12T18:30:00Z