The Laplace-Beltrami Operator on a Rotationally Symmetric Surface
The aim of this work is to highlight a number of analytic problems which make the analysis on manifolds with true cuspidal points much more difficult than that on manifolds with conic points while such singularities are topologically equivalent. To this end we discuss the Laplace-Beltrami operator on a compact rotationally symmetric surface with a complete metric. Even though the symmetry assumptions made here lead to a simplified situation in which standard separation of variables works, it is hoped that the study of this example can nevertheless bring to light some features which may subsist in the more general framework of the calculus on compact manifolds with cusps due to V. Rabinovich et al. (1997).
Mathematics Subject Classification (2000)Primary 58-XX Secondary 47-XX.
KeywordsManifolds with singularities pseudodifferential operators ellipticity
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