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

Ovidiu Calin,Irina Markina,Der-Chen Chang

doi:10.1007/978-3-7643-9906-1_3

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

Ovidiu Calin, Irina Markina + Show 1 more

https://doi.org/10.1007/978-3-7643-9906-1_3

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Publication Date: Jan 1, 2009

Citations: 11

Affiliation: Eastern Michigan University, University of Bergen, National Center for Theoretical Sciences, National Tsing Hua University, Georgetown University

#Step Nilpotent Lie Groups #Generalized Hamilton Jacobi Equation + Show 8 more

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Abstract

AbstractWe 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.Mathematics Subject Classification (2000)53C1753C2235H20KeywordsSub-LaplacianHeat operatorH-type groupsaction functionvolume element

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