Surfaces of Constant Mean Curvature Which Have a Simple Projection.
Surfaces of Prescribed Mean Curvature with Inequalities on the Boundary.
Surfaces which contain many circles
We survey the results on surfaces which contain many circles. First, we give two analyses of shapes which always look round. Then we introduce the Blum conjecture: “A closed surface in E³ which contains seven circles through each point is a sphere”, and give some partial affirmative results toward the conjecture. Moreover, we study some surfaces which contain many circles through each point, for example, cyclides.
Surfaces with Parallel Normalized Mean Curvature Vector.
Surfaces with prescribed Weingarten operator
We investigate pairs of surfaces in Euclidean 3-space with the same Weingarten operator in case that one surface is given as surface of revolution. Our local and global results complement global results on ovaloids of revolution from S-V-W-W.