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CATEGORIES:Analysis Seminar
SUMMARY:Conformal Immersions into Riemannian Manifolds - H
uy The Nguyen\, Queen Mary University of London
DTSTART:20180122T140000Z
DTEND:20180122T150000Z
UID:TALK3028AT
URL:/talk/index/3028
DESCRIPTION: We develop the geometry and analysis of conform
al immersions of surfaces into an a Riemannian man
ifold. We show an optimal Wente estimate for the L
iouville Equation and as a consequence prove a sin
gularity removal theorem for isolated singularitie
s of conformal surfaces. This is used to extend a
theorem of B. White to the setting of immersions o
f Riemannian manifolds. Next we prove a formula fo
r the the Gauss Bonnet theorem and the conformal W
illmore energy under conformal deformations of the
ambient metric that generalises the conformal inv
ariance of the Euclidean Willmore energy. A local
compactness theorem is proved with optimal constan
ts if n ≥ 4 and an energy identity is proved for t
he Gauss-Bonnet energy in the presence of a single
bubble. This is used to obtain the optimal consta
nt for n = 3. Finally we prove a geometric rigidit
y theorem for the generalised total curvature inte
gral\, showing that if we attain the optimal const
ant in the local compactness theorem but lose weak
compactness then this is due to the presence of a
complete compact minimal surface in Rn.\n\n
LOCATION:Nuffield G19
CONTACT:Yuzhao Wang
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