On the Heat Equation and the Index Theorem.
M. Atiyah, R. Bott, V.K. Patodi (1973)
Inventiones mathematicae
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Displaying similar documents to “The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs.”
On the Heat Equation and the Index Theorem.
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Harold Donnelly (1975)
Inventiones mathematicae
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Stochastic Taylor expansions and heat kernel asymptotics
Fabrice Baudoin (2012)
ESAIM: Probability and Statistics
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These notes focus on the applications of the stochastic Taylor expansion of solutions of stochastic differential equations to the study of heat kernels in small times. As an illustration of these methods we provide a new heat kernel proof of the Chern–Gauss–Bonnet theorem.