217 research outputs found
Weighted -Liouville Theorems for Hypoelliptic Partial Differential Operators on Lie Groups
We prove weighted -Liouville theorems for a class of second order
hypoelliptic partial differential operators on Lie groups
whose underlying manifold is -dimensional space. We show that a
natural weight is the right-invariant measure of . We
also prove Liouville-type theorems for subsolutions in
. We provide examples of operators to which our
results apply, jointly with an application to the uniqueness for the Cauchy
problem for the evolution operator
A Hadamard-type open map theorem for submersions and applications to completeness results in Control Theory
We prove a quantitative openness theorem for submersions under suitable
assumptions on the differential. We then apply our result to a class of
exponential maps appearing in Carnot-Carath\'eodory spaces and we improve a
classical completeness result by Palais.Comment: 12 pages. Revised version. Minor changes. To appear on Annali di
Matematic
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