A duality theorem for Willmore surfaces,
J. Differential Geom., vol. 20 no. 1
(1984),
pp. 23–53 [MR86j:58029]
(last updated on 2004/04/06)
Author's Comments:
A study of surface theory in conformal 3-space, 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 2-spheres
are shown to be discrete and the moduli space of the
extrema having the
first non-minimal 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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