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UID:7149@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20190111T110000
DTEND;TZID=Europe/Paris:20190111T133000
DTSTAMP:20241207T133203Z
URL:https://www.i2m.univ-amu.fr/evenements/the-marked-length-spectrum-of-a
 nosov-manifolds-colin-guillarmou/
SUMMARY:Colin Guillarmou (LMO\, Université Paris-Saclay): The marked lengt
 h spectrum of Anosov manifolds
DESCRIPTION:Colin Guillarmou: Exposé commun du séminaire de Probabilités
  et du séminaire Teich.\nIn all dimensions\, we prove that the marked len
 gth spectrum of a Riemannian manifold (M\,g) with Anosov geodesic flow and
  non-positive curvature locally determines the metric in the sense that tw
 o close enough metrics with the same marked length spectrum are isometric.
  In addition\, we provide a completely new stability estimate quantifying 
 how the marked length spectrum control the distance between the metrics. I
 n dimension 2 we obtain similar results for general metrics with Anosov ge
 odesic flows. We also solve locally a rigidity conjecture of Croke relatin
 g volume and marked length spectrum for the same category of metrics. Fina
 lly\, by a compactness argument\, we show that the set of negatively curve
 d metrics (up to isometry) with the same marked length spectrum and with c
 urvature in a bounded set of C∞ is finite.\nhttps://arxiv.org/abs/1806.0
 4218\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Colin_Guillarmou.jpg
CATEGORIES:Séminaire,Probabilités,Rauzy
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