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Hypoelliptic Laplacian and Orbital Integrals (AM-177) by Jean-Michel Bismut

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Chapter Fourteen

The heat kernel image for bounded b

The purpose of this chapter is to establish the estimates of Theorem 4.5.2 for the hypoelliptic heat kernel image ((x, Y), (x′, Y′)) on image. More precisely, we show that for bounded b > 0, the heat kernel verifies uniform Gaussian type estimates. Also we study the limit as b → 0 of this heat kernel.

The method consists in using the techniques of chapters 12 and 13 for the scalar heat kernels over and , and to ...

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