BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Partial Differential Equations seminar
SUMMARY:Mean curvature flow for spacelike surfaces\, holom
orphic discs and the Caratheodory Conjecture. - Wi
lhelm Klingenberg (Durham)
DTSTART;TZID=Europe/London:20100208T160000
DTEND;TZID=Europe/London:20100208T170000
UID:TALK22902AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/22902
DESCRIPTION:We outline joint work with Brendan Guilfoyle\, whi
ch establishes a proof of\nthe Caratheodory Conjec
ture. This claims that every C3 - differentiable\n
sphere in Euclidean space admits at least two umbi
lic points. (These are\nlocally spherical points\;
at such points both principal curvatures are\nequ
al\, and every tangent vector is a principal direc
tion).\nRemark: This is one more umbilic than need
s to appear for topological\nreasons\, namely the
nonvanishing of the Euler number of the sphere (th
ereby\npresents an instance of rigidity).\nOur pro
of is inspired by Gromov's symplectic rigidity-fle
xibility dichotomy\n(specifically by his approach
to the rigidity of convex surfaces which lead\nhim
to the development of his theory of pseudoholomor
phic curves). It uses\nnew a - priory gradient est
imates for Mean Curvature Flow in manifolds of\nsp
lit signature (building on work of Bartnik and Eck
er-Huisken). The latter\nallows us to construct a
holomorphic disc with boundary encircling an\nisol
ated umbilic point (in a symplectic model space).
This results in\nsufficient rigidity to prove CC i
n the spirit of said dichotomy.\n
LOCATION:CMS\, MR15
CONTACT:Prof. Neshan Wickramasekera
END:VEVENT
END:VCALENDAR