Hypersurfaces with constant inner curvature of the second fundamental form, and the non-rigidity of the sphere.
Hypersurfaces with constant scalar curvature in space forms.
Immersions with a parallel normal field.
Inequalities of Willmore Type for Submanifolds.
Infinitesimal rigidity of Euclidean submanifolds
A submanifold of the Euclidean space is said to be infinitesimally rigid if any smooth variation which is isometric to first order is trivial. The main purpose of this paper is to show that local or global conditions which are well known to imply isometric rigidity also imply infinitesimal rigidity.
Interior estimates for hypersurfaces moving by mean curvature.
Invariants and Bonnet-type theorem for surfaces in ℝ4
In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes of surfaces...
Invariants and canonical equations of hypersurfaces of second order in -dimensional Euclidean space.
Involute-evolute curve couples in the Euclidean 4-space.
Isometric immersions of domains of Lobachevski space in Euclidean spaces
Isometrische Immersionen des n-dim. hyperbolischen Raumes Hn in E4n-3.
Isothermic surfaces and Hopf cylinders.
k-Symmetric Submanifolds of RN.
Local gradient estimates of -harmonic functions, -flow, and an entropy formula
In the first part of this paper, we prove local interior and boundary gradient estimates for -harmonic functions on general Riemannian manifolds. With these estimates, following the strategy in recent work of R. Moser, we prove an existence theorem for weak solutions to the level set formulation of the (inverse mean curvature) flow for hypersurfaces in ambient manifolds satisfying a sharp volume growth assumption. In the second part of this paper, we consider two parabolic analogues of the -harmonic...
Local isometric immersions of R2 into R4.
Lokale Kennzeichnungen der Minimalhyperregelflächen.
Mean directionally curved lines on surfaces immersed in R4.
The notion of principal configuration of immersions of surfaces into R3, due to Sotomayor and Gutierrez [16] for lines of curvature and umbilics, is extended to that of mean directional configuration for immersed surfaces in R4. This configuration consists on the families of mean directionally curved lines, along which the second fundamental form points in the direction of the mean curvature vector, and their singularities, called here H-singularities.
Measurability of classes of Lipschitz manifolds with respect to Borel -algebra of Vietoris topology
Minding-Isometrien bei (k + 1)-Regelflächen.
Minimal solutions of variational problems on a torus