Homogeneous surfaces in the equiaffine space R⁴
Homogeneous systems of higher-order ordinary differential equations
The concept of homogeneity, which picks out sprays from the general run of systems of second-order ordinary differential equations in the geometrical theory of such equations, is generalized so as to apply to equations of higher order. Certain properties of the geometric concomitants of a spray are shown to continue to hold for higher-order systems. Third-order equations play a special role, because a strong form of homogeneity may apply to them. The key example of a single third-order equation...
How to blow infinitely large soap bubbles with a fixed boundary
How to unify the total/local-length-constraints of the gradient flow for the bending energy of plane curves
The gradient flow of bending energy for plane curve is studied. The flow is considered under two kinds of constraints; one is under the area and total-length constraints; the other is under the area and local-length constraints. The fundamental results (the local existence and uniqueness) were obtained independently by Kurihara and the second author for the former one; by Okabe for the later one. For the former one the global existence was shown for any smooth initial curves, but the asymptotic...
H-surface index formula
Hyperbolic geometry in hyperbolically k-convex regions
Hyperbolicity of the Complement of Plane Curves.
Hyperbolization of Euclidean ornaments.
Hypersurface geometry and Hamiltonian systems of hydrodynamic type.
Hypersurfaces in 4-dimensional Euclidean space
Hypersurfaces of prescribed mean curvature enclosing a given body.
Hypersurfaces with almost complex structures in the real affine space
We study affine hypersurface immersions , where M is an almost complex n-dimensional manifold. The main purpose is to give a condition for (M,J) to be a special Kähler manifold with respect to the Levi-Civita connection of an affine fundamental form.
Hypersurfaces with constant curvature in
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.
Hypersurfaces with constant inner curvature of the second fundamental form, and the non-rigidity of the sphere.
Hypersurfaces with constant -th mean curvature in a Lorentzian space form
In this paper, we study -dimensional complete connected and oriented space-like hypersurfaces in an (n+1)-dimensional Lorentzian space form with non-zero constant -th mean curvature and two distinct principal curvatures and . We give some characterizations of Riemannian product and show that the Riemannian product is the only complete connected and oriented space-like hypersurface in with constant -th mean curvature and two distinct principal curvatures, if the multiplicities of...
Hypersurfaces with Constant Mean Curvature and Prescribed Area.
Hypersurfaces with constant scalar curvature in a hyperbolic space form.
Hypersurfaces with constant scalar curvature in space forms.
Hypersurfaces with constant scalar or mean curvature in a unit sphere.
Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds
Given a domain of and a -dimensional non-degenerate minimal submanifold of with , we prove the existence of a family of embedded constant mean curvature hypersurfaces in which as their mean curvature tends to infinity concentrate along and intersecting perpendicularly along their boundaries.