A lower estimate for the number of zero-torsion points of a space curve.
A maximum principle for mean-curvature type elliptic inequalities
A measure of symmetry for ovals
A Method of Solving Nonlinear Variational Problems by Nonlinear Transformation of the Objective Functional. Part II.
A Method of Solving Nonlinear Variational Problems by Nonlinear Transformation of the Objective Functional. Part I.
A metric induced by the geometric interpretation of Rolle's theorem.
A Monge-Ampère equation in conformal geometry
We consider the Monge-Ampère-type equation , where is the Schouten tensor of a conformally related metric and is a suitably chosen constant. When the scalar curvature is non-positive we give necessary and sufficient conditions for the existence of solutions. When the scalar curvature is positive and the first Betti number of the manifold is non-zero we also establish existence. Moreover, by adapting a construction of Schoen, we show that solutions are in general not unique.
A new approach for describing instantaneous line congruence
Based on the E. Study’s map, a new approach describing instantaneous line congruence during the motion of the Darboux frame on a regular non-spherical and non-developable surface, whose parametric curves are lines of curvature, is proposed. Afterward, the pitch of general line congruence is developed and used for deriving necessary and sufficient condition for instantaneous line congruence to be normal. In terms of this, the derived line congruences and their differential geometric invariants were...
A New Approach to the Theory of the Riemann Space
A new characterization of the sphere in
Let M be a closed connected surface in with positive Gaussian curvature K and let be the curvature of its second fundamental form. It is shown that M is a sphere if , for some constants c and r, where H is the mean curvature of M.
A New Conformal Invariant and Its Applications to the Wilmore Conjecture and the First Eigenvalue of Compact Surfaces.
A new intrinsic curvature invariant for centroaffine hypersurfaces.
A new model of unimodular-affinely homogeneous surfaces.
A new obstruction to minimal isometric immersions into a real space form.
A new proof of the gardient estimate for graphs of prescribed mean curvature.
A non-existence theorem for stable constant mena curvature hypersurfaces.
A non-homogeneous, symmetric contact projective structure
We construct a non-homogeneous contact projective structure which is symmetric from the point of view of parabolic geometries.
A non-standard approach to the Euclidean study of plane curves.
A nonstandard characterization of regular surfaces.
A nonstandard-analysis characterization of submanifolds in Euclidean space.