Kazuo Akutagawa

Remarks on the Gauss images of complete minimal surfaces in Euclidean four-space

We perform a systematic study of the image of the Gauss map for complete minimal surfaces in Euclidean four-space. In particular, we give a geometric interpretation of the maximal number of exceptional values of the Gauss map of a complete orientable minimal surface in Euclidean four-space. We also provide optimal results for the maximal number of exceptional values of the Gauss map of a complete minimal Lagrangian surface in the complex two-space and the generalized Gauss map of a complete nonorientable minimal surface in Euclidean four-space.

A gap theorem for positive Einstein metrics on the four-sphere

We show that there exists a universal positive constant

3-manifolds with positive flat conformal structure

\varepsilon _0 > 0

On Yamabe constants of Riemannian products

ε0>0 with the following property: let g be a positive Einstein metric on the four-sphere

The Yamabe problem on stratified spaces

S^4

\RP^3

S4. If the Yamabe constant of the conformal class [g] satisfies