Sub-elliptic PDEs and
sub-Riemannian Geometry
Professor Der-Chen Chang
Abstract
In this
talk, we propose a structure for inverse kernels---fundamental solutions, heat
kernels, etc. ─ of second order partial differential operators given as sums of
squares of vector fields. The formulas are built from invariants of the
underlying geometry induced by the given vector fields. We shall assume that
brackets of these vector fields yield the tangent space, thus Chow's theorem
gives a distance function and a subRiemannian
geometry. The main object of interest is a complex distance, parametrized by the characteristic variety, whose critical
points along the characteristic variety yield geodesics. We shall illustrate
these ideas by examples.
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Room 517, Meng Wah Complex, HKU |
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All are
welcome |
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