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Displaying 101 –
120 of
328
This paper concerns projectively Anosov flows with smooth stable and unstable
foliations and on a Seifert manifold . We show that if the
foliation or contains a compact leaf, then the flow is
decomposed into a finite union of models which are defined on and
bounded by compact leaves, and therefore the manifold is homeomorphic to the 3-torus.
In the proof, we also obtain a theorem which classifies codimension one foliations on
Seifert manifolds with compact leaves which are incompressible...
2000 Mathematics Subject Classification: 49J15, 49J30, 53B50.In the context of sub-Riemannian geometry and the Lipschitzian regularity of minimizers in control theory, we investigate some properties of minimizing geodesics for certain affine distributions. In particular, we consider the case of a generalized H2-strong affine distribution and the case of an affine Plaff system of maximal class.
We formulate an Hamilton-Jacobi partial differential equationon a dimensional manifold , with assumptions of convexity of and regularity of (locally in a neighborhood of in ); we define the “min solution” , a generalized solution; to this end, we view as a symplectic manifold. The definition of “min solution” is suited to proving regularity results about ; in particular, we prove in the first part that the closure of the set where is not regular may be covered by a countable number...
This errata corrects one error in the 2004 version of this paper [Mennucci, ESAIM: COCV10 (2004) 426–451].
We formulate an Hamilton-Jacobi partial differential equation
H( x, D u(x))=0
on a n dimensional manifold M, with
assumptions of convexity of H(x, .) and regularity of
H (locally in a neighborhood of {H=0} in T*M); we define the
“minsol solution” u, a generalized solution;
to this end, we view T*M
as a symplectic manifold.
The definition of “minsol solution” is suited to proving
regularity results about u; in particular, we prove
in the first part that the
closure of the set where...
This article addresses regularity of optimal transport maps for cost=“squared distance” on Riemannian manifolds that are products of arbitrarily many round spheres with arbitrary sizes and dimensions. Such manifolds are known to be non-negatively cross-curved. Under boundedness and non-vanishing assumptions on the transfered source and target densities we show that optimal maps stay away from the cut-locus (where the cost exhibits singularity), and obtain injectivity and continuity of optimal maps....
Given a continuous viscosity solution of a Dirichlet-type Hamilton-Jacobi equation, we show that the distance function to the conjugate locus which is associated to this problem is locally semiconcave on its domain. It allows us to provide a simple proof of the fact that the distance function to the cut locus associated to this problem is locally Lipschitz on its domain. This result, which was already an improvement of a previous one by Itoh and Tanaka [Trans. Amer. Math. Soc. 353 (2001) 21–40],...
Currently displaying 101 –
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328