Abstract
The method of construction of the fundamental solution for the heat equations of the initial boundary value problem on manifolds with boundary, which is applicable to calculate traces of operators, is discussed. This shows a relation of the singularity of the fundamental solution and the curvature of manifolds. We may say that this is an extension of a local version of Gauss-Bonnet-Chern theorem for manifolds with boundary.
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Iwasaki, C. (2008). Construction of the Fundamental Solution and Curvature of Manifolds with Boundary. In: Rodino, L., Wong, M.W. (eds) New Developments in Pseudo-Differential Operators. Operator Theory: Advances and Applications, vol 189. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8969-7_4
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DOI: https://doi.org/10.1007/978-3-7643-8969-7_4
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