**Papers Published**

- Bryant, RL,
*A duality theorem for willmore surfaces*, Journal of Differential Geometry, vol. 20 no. 1 (January, 1984), pp. 23-53, International Press of Boston

(last updated on 2019/05/25)**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.