Geometric Analysis and Topology Seminar

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Closed curves of constant geodesic curvature on the two-sphere

Speaker: Rohil Prasad, Princeton University

Location: Warren Weaver Hall 512

Date: Friday, February 6, 2026, 11 a.m.

Synopsis:

For any Riemannian metric on the two-sphere and a full Lebesgue measure set of constants k, we show that there exist at least two distinct closed curves of constant geodesic curvature k. This is related to a question of Arnold from 1981. The proof uses some old and new ideas from symplectic geometry.