DIFFERENTIAL GEOMETRY/PDE SEMINAR

Thursday, February 12, 2004 Padelford C-36 1:30 pm

Sharp isoperimetric questions and rigidity problems

Christopher Croke (University of Pennsylvania)

In this talk we discuss some open sharp isoperimetric questions and conjectures. For manifolds with boundary they are of ”filling-volume type” while for closed manifolds they are lower bounds on the volume in terms of the marked length spectrum. The case of equality in the inequalities is related to some long standing rigidity questions (boundary rigidity and geodesic conjugacy rigidity respectively). Recent work on these questions in two dimensions (joint with Dairbekov and joint with Bangert, Ivanov, and Katz) will be presented. (The talk should be accessible to graduate students.)

For more information about this seminar, visit the DG/PDE Seminar Web page (from the Math Department home page, www.math.washington.edu, follow the link Seminars, Colloquia, and Conferences).

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