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UID:20260710T064718EDT-7990uDe9fw@132.216.98.100
DTSTAMP:20260710T104718Z
DESCRIPTION:Vincent Grandjean\,\nFields Institute\nAssume a Riemannian mani
 fold (M\,g) is given. Let X be a\nlocally closed subset of M\, that is sin
 gular at some of its point\,\nthat is X is not a submanifold at this point
 . We can think of\nsingular real algebraic sets\, or germs or real analyti
 c sets as a\nmodel of the singularities we are interested in dealing with.
  The\nsmooth part of X comes equipped with a Riemannian metric induced\nfr
 om the ambient one. We would like to understand how do geodesics\non the r
 egular part of X behave in a neighbourhood of a singular\npoint. It turns 
 out that very little is known (or even explored)\nabout very elementary si
 ngularities (conical\, edges or corners).\nThe purpose of specifying such 
 a singular set was to study the\npropagation of singularities for the wave
  equation on such a\nsingular 'manifold' (Melrose\, Vasy\, Wunsch\,...). I
 n this joint work\nwith Daniel Grieser (Oldenburg\, Germany)\, we want to 
 address a\nnaive and elementary question: Given an isolated surface\nsingu
 larity X in (M\,g)\, can a neighbourhood of the singular point\nbe foliate
 d by geodesics reaching the singular point ? Then can we\ndefine an expone
 ntial mapping at a such point ? This property is\ntrue for conical singula
 rities of any dimension. With D. Grieser\,\nwe have exhibited very simple 
 examples of non-conical real surfaces\nwith an isolated singularity\, and 
 cuspidal like\, in a 3-manifold\,\nsuch that the geodesics reaching the si
 ngular point behave\ndifferently according to the considered class.\n
DTSTART:20110211T193000Z
DTEND:20110211T213000Z
LOCATION:Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue Sherbrooke 
 Ouest
SUMMARY:Geodesics at singular points of singular subspaces: a few striking 
 examples
URL:/channels/event/geodesics-singular-points-singular
 -subspaces-few-striking-examples-171453
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