講演タイトル・アブストラクトおよびプログラム：

2014年1月9日（木）

Franz Pedit (Tuebingen University)

13:30-15:00 "Constrained Willmore Surfaces: Theory and Experiment"

Constrained Willmore surfaces are critical points for the Willmore energy under variations of the surface preserving its conformal structure. We will explain the (very few) known results for compact surfaces in general and then focus on the case of tori. Here theoretical results and experimental work (equivariant examples, conformal Willmore flow) come together to suggest a first picture of what a "constrained Willmore conjecture" might look like.

Katsuhiro Moriya (University of Tsukuba)

15:15-16:45 "Some Results about Twistor Holomorphic Maps"

A map from an almost Hermitian manifold to an even dimensional Riemannian manifold is called twistor holomorphic if it has a lift to the twistor space and it is holomorphic with respect to almost complex structures. A twistor lift is used to investigate conformal geometry of a twistor holomorphic map. I will report recent results about twistor holomorphic maps by Japanese mathematicians.

2014年1月10日（金）

Franz Pedit (Tuebingen University)

13:30-15:00 "Conformal Willmore Flow"

We will construct a flow on compact surfaces which preserves the conformal type and decreases the Willmore energy. In good cases this flow will push the compact surface to a constrained Willmore minimizer. An interesting feature of this flow is that it preserves derivatives, in other words, it can be regarded as an ODE on any of the Hoelder spaces. This makes this flow analytically much easier to study than the usual L^2 Willmore gradient flow. We will explain this flow first on closed plnar curves as an alternative to the curve straightening and curve shortening flows. The surface version of the flow is then constructed in a similar way using the mean curvature half density of the surface (instead of the curvature in the case of planar curves).