Chapter

# Generalized Hamilton—Jacobi Equation and Heat Kernel on Step Two Nilpotent Lie Groups

DOI: 10.1007/978-3-7643-9906-1_3 In book: Analysis and Mathematical Physics, pp.49-76

**ABSTRACT**

We study geometrically invariant formulas for heat kernels of subelliptic differential operators on two step nilpotent Lie

groups and for the Grusin operator in ℝ2. We deduce a general form of the solution to the Hamilton—Jacobi equation and its generalized form in ℝn × ℝm. Using our results, we obtain explicit formulas of the heat kernels for these differential operators.

groups and for the Grusin operator in ℝ2. We deduce a general form of the solution to the Hamilton—Jacobi equation and its generalized form in ℝn × ℝm. Using our results, we obtain explicit formulas of the heat kernels for these differential operators.

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