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A heat trace anomaly on polygons Rafe Mazzeo
 

Summary: A heat trace anomaly on polygons
Rafe Mazzeo
Stanford University
Julie Rowlett
UC Santa Barbara
Abstract
Let 0 be a polygon in R2
, or more generally a compact surface with
piecewise smooth boundary and corners. Suppose that is a family
of surfaces with C
boundary which converges to 0 smoothly away
from the corners, and in a precise way at the vertices to be described
in the paper. Both Kac [3] and McKean-Singer [7] recognized that
certain heat trace coefficients, in particular the coefficient of t0
, are not
continuous as 0. We describe this anomaly using renormalized heat
invariants of an auxiliary smooth domain Z which models the corner
formation.
1 Introduction
Let R2 be a domain with smooth boundary, or more generally, any two

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics