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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The space of soap bubbles - Kusner\, R (University
of Massachusetts)
DTSTART;TZID=Europe/London:20121120T113000
DTEND;TZID=Europe/London:20121120T123000
UID:TALK41569AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/41569
DESCRIPTION:Understanding the space of all 'soap bubbles' - th
at is\, complete embedded constant mean curvatures
(CMC) surfaces in $R^3$ - is a central problem in
geometric analysis. These CMC surfaces are highly
transcendental objects\; the topology and smooth
structure of their moduli spaces are understood on
ly in some special cases. In this talk we will des
cribe the formal 'Lagrangian embedding' of CMC mod
uli space into the 'space of asymptotes' \nand dis
cuss where this is smooth\, namely\, at a surface
with no nontrivial square-integrable Jacobi fields
. This nondegeneracy condition has now been establ
ished for all coplanar CMC surfaces of genus zero\
; this allows them to serve as 'building blocks' f
or more complicated CMC surfaces. There is also a
surprising connection with complex projective stru
ctures and holomorphic quadratic differentials on
$C$ obtained by taking the Schwarzian of the devel
oping map for the projective structure. This assig
ns each coplanar CMC surface a 'classifying' compl
ex polynomial\, and lets us explicitly work out th
e smooth topology of their moduli spaces.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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