Geodesics in heat
نویسندگان
چکیده
منابع مشابه
Geodesics in Heat
We introduce the heat method for computing the shortest geodesic distance to an arbitrary subset of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The resulting algorithm represents a significant breakthrough in the practical computation of distance on a wide variety of geometric domains, si...
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We use the gradient flow on the path space to obtain estimates on the heat kernel k(t, x, y) on a complete Riemannian manifold. This approach gives a sharp formula for the small-time asymptotics of k(t, x, y) and an upper bound for all time for pairs x and y are not conjugate. It also gives a theorem about convolutions of heat kernels that makes precise the intuition that heat flows in packets ...
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On a closed Riemannian manifold pM, gq, the geodesic heat flow deforms loops through an energydecreasing homotopy uptq. It is known that there is a sequence tn Ñ 8 so that uptnq converges in C to a closed geodesic, but it is also known that convergence fails in general. We show that for a generic set of metrics on M , the heat flow converges for all initial loops. We also show that convergence,...
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The geodesic equations are integrated for the Lewis metric and the effects of the different parameters appearing in the Weyl class on the motion of test particles are brought out. Particular attention deserves the appearance of a force parallel to the axial axis and without Newtonian analogue.
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Let M be a Margulis spacetime whose associated complete hyperbolic surface Σ has compact convex core. Generalizing the correspondence between closed geodesics on M and closed geodesics on Σ, we establish an orbit equivalence between recurrent spacelike geodesics on M and recurrent geodesics on Σ. In contrast, no timelike geodesic recurs in neither forward nor backwards time.
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ژورنال
عنوان ژورنال: ACM Transactions on Graphics
سال: 2013
ISSN: 0730-0301,1557-7368
DOI: 10.1145/2516971.2516977