A geometric characterization of the orbits of s-representations.
A geometric estimate for a periodic Schrödinger operator
We estimate from below by geometric data the eigenvalues of the periodic Sturm-Liouville operator with potential given by the curvature of a closed curve.
A geometric problem and the Hopf Lemma. I
A classical result of A. D. Alexandrov states that a connected compact smooth -dimensional manifold without boundary, embedded in , and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of in a hyperplane in case satisfies: for any two points , on , with , the mean curvature at the first is not greater than that at the second. Symmetry need not always hold, but in this paper, we establish it under some additional condition for . Some variations...
A holomorphic representation formula for parabolic hyperspheres
A holomorphic representation formula for special parabolic hyperspheres is given.
A homological characterization of foliations consisting of minimal surfaces.
A limiting geometry for capillary surfaces
A local characterization of affine holomorphic immersions with an anti-complex and ∇-parallel shape operator
We study the complex hypersurfaces which together with their transversal bundles have the property that around any point of M there exists a local section of the transversal bundle inducing a ∇-parallel anti-complex shape operator S. We give a class of examples of such hypersurfaces with an arbitrary rank of S from 1 to [n/2] and show that every such hypersurface with positive type number and S ≠ 0 is locally of this kind, modulo an affine isomorphism of .
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.