Lecture Event
Proof of the Caratheodory Conjecture, Part II
Brendan Guilfoyle (Tralee/ Ireland)
21 Jan 2009, 16:30 – 17:30
In these two self-contained talks we outline a proof of the Caratheodory
conjecture,
which states that there must be at least 2 umbilic points on a closed
convex surface in Euclidean 3-space. The proof involves a reformulation
of the Conjecture in terms of the index of a complex point on a
Lagrangian surface in TS2, and establishing the existence of
holomorphic discs with boundary lying on the Lagrangian surface.
In this second talk we establish the existence of the holomorphic discs by
using mean curvature flow with respect to the neutral Kaehler metric on
TS2.
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