Flächen vorgeschriebener mittlerer Krümmung mit eindeutiger Projektion auf eine Ebene.
We study the global behavior of foliations of ellipsoids by curves making a constant angle with the lines of curvature.
The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions.
We study rolling maps of the Euclidean ellipsoid, rolling upon its affine tangent space at a point. Driven by the geometry of rolling maps, we find a simple formula for the angular velocity of the rolling ellipsoid along any piecewise smooth curve in terms of the Gauss map. This result is then generalised to rolling any smooth hyper-surface. On the way, we derive a formula for the Gaussian curvature of an ellipsoid which has an elementary proof and has been previously known only for dimension two....
We give some optimal estimates of the height, curvature and volume of compact hypersurfaces in with constant curvature bounding a planar closed (n-1)-submanifold.