Math @ Duke

Publications [#243393] of Robert Bryant
search www.ams.org.Papers Published
 Bryant, RL, A duality theorem for Willmore surfaces,
J. Differential Geom., vol. 20 no. 1
(1984),
pp. 2353 [MR86j:58029]
(last updated on 2018/07/16)
Author's Comments: A study of surface theory in conformal 3space, with an
application
to the extremals of the Willmore functional, which can
be thought of as
the conformal area of a surface in this geometry.
Among the results are a proof that every compact
extremal of genus 0
is conformally a minimal surface. This relies on a
vanishing theorem plus
a careful analysis of the singularities of the geometry
near the `umbilic'
points. Also the critical values of the Willmore functional
on 2spheres
are shown to be discrete and the moduli space of the
extrema having the
first nonminimal critical value is computed.
Since this paper, much has been done. For an
update, see Surfaces in Conformal Geometry.
Lucas Hsu kindly compiled a list of
errata and has allowed me to include an amstex
version of it here.
Reprints are available.


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