2009 / June Volume 4 No.2
Geometric analysis on a step 2 Grusin operator
| Published Date |
2009 / June
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| Title | Geometric analysis on a step 2 Grusin operator |
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| Pagination | 119-188 |
| Abstract | The Grusin operator $\Delta G \ = \ \frac 12 (\partial^2_x + x^2\partial^2_y), \ x,y \ \in \ \mathbb{R}$, is studied by Hamilton-Jacobi theory. In particular, we find all the
geodesics of $\Delta G$ of the induced nonholonomic geometry, construct a modified complex action $f$ which allows us to obtain the heat kernel $P_t$ of $\Delta G$. The small time asymptotics of $P_t$ at all critical points of $f$ are computed. Finally we discuss the connection between $\Delta G$ and the subLaplacian of the 1-dimensional Heisenberg group.
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| AMS Subject Classification |
53C17, 34K10, 25H20
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| Received |
2009-05-12
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| Accepted |
2009-05-12
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