Tel Aviv University
The next colloquium talk will be held on Monday, 16/4/2012, 12:15, Schreiber
006, Tel Aviv University. The speaker is
Victor Palamodov (Tel Aviv University)
and the title of his talk is
Inverse kinematic problem and rigidity of Riemannian metrics
The abstract is given below. Tea and coffee at 12:00, same room.
Hope to see you there. For information about future colloqiua, see
You are all welcome to suggest colloquium speakers for this semester.
Abstract: We are given a compact domain with boundary (e. g. a ball) with an
unknown conformal Euclidean metric. The problem is to reconstruct the metric
from knowledge of lengths of all closed geodesics in the domain. This
problem was formulated more than hundred years ago in geophysics, where the
length of a geodesic is called travel-time. An explicit reconstruction of an
isotropic velocity field from travel-times was found by G. Herglotz for the
spheric Earth model with velocity depending only on depth.
Much later, in the seventies progress in theoretical geophysics (Novosibirsk
group, Bernstein, Gerver, Beylkin) gave rise a problem of Riemannian
geometry: in which extent a Riemannian metric on a manifold with boundary
can be determined from its travel-time function? Finally an answer was found
for metrics within a given conformal class.
If the conformal class is not known then a unique determination of a metric
is not possible because of shortage of information. A natural question is
whether a Riemannian metric in a manifold is rigid with respect to lengths
of all closed geodesics (Michel, Gromov, Pestov, Uhlmann,...). The rigidity
problem is still far from a complete solution.
More tags: Santalo's volume formula, "Goursat theorem" for a geodesic
geometry, integral geometry.
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel <email@example.com>
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