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Home » Geometry: Bernstein type theorems for the Willmore surface equation

Seminar

Geometry: Bernstein type theorems for the Willmore surface equation March 30, 2016 (11:00 AM PDT - 12:00 PM PDT)
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Location: MSRI: Baker Board Room
Speaker(s) Jingyi Chen (University of British Columbia)
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Abstract/Media

A Willmore surface in the 3-dimensional Euclidean space is a critical point of the square norm of the mean curvature of the surface.

The round spheres, the Clifford torus and the minimal surfaces are Willmore. For a graph to satisfy the Willmore surface equation, its defining function is governed by a fourth order non-linear elliptic equation. A classical theorem of Bernstein says that an entire minimal graph must be a plane. We ask what happens to the entire Willmore graphs. In this talk, I will discuss joint work with Tobias Lamm on the finite energy case and with Yuxiang Li on the radially symmetric case.

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