# From 1-homogeneous supremal functionals to difference quotients: relaxation and G-convergence

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Let F a three-dimensional body of constant width B. Then the geodesic diameter G of the surface of F is estimated via B from above and from below. It is proved that $$ G \leqslant \frac{\pi }{2}B $$, where an equality occurs and only if F is a body of revolution. Bibliography: 3 titles.

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Expansions of the gravitational field arising from the development of asymptotically Euclidean, time symmetric, conformally flat initial data are calculated in a neighbourhood of spatial and null infinities up to order 6. To this end a certain representation of spatial infinity as a cylinder is...

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It is proved that non-degenerate surfaces in R4 with planar geodesics are only the complex paraboloid and the product of two parabolas.

- Geodesic Ham-Sandwich Cuts. Prosenjit Bose; Erik D. Demaine; Ferran Hurtado; John Iacono; Stefan Langerman; Pat Morin // Discrete & Computational Geometry;Mar2007, Vol. 37 Issue 3, p325
Abstract??Let P be a simple polygon with m vertices, k of which are reflex, and which contains r red points and b blue points in its interior. Let n = m r b. A ham-sandwich geodesic is a shortest path in P between two points on the boundary of P that simultaneously bisects the red points and...

- Classification of two-dimensional totally geodesic submanifolds in the Grassmannian G. Nikanorovo, M. // Journal of Mathematical Sciences;Sep2009, Vol. 161 Issue 3, p443
The classification mentioned in the title is explicitly described. Bibliography: 9 titles.

- Visibility metrics on the infinity boundary of the complex hyperbolic plane. Kuznetsov, A. // Journal of Mathematical Sciences;Sep2009, Vol. 161 Issue 3, p392
Limiting spherical and horospherical metrics an the infinity boundary of the complex hyperbolic plane are constructed. It is proved that the limiting spherical metric, which automatically is the Carnotï¿½Carathï¿½odory metric, is also a visibility metric, i.e., it belongs to a canonical...

- On geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1. Zelenko, I. // Journal of Mathematical Sciences;Jun2006, Vol. 135 Issue 4, p3168
The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using the Pontryagin maximum principle, we treat Riemannian and sub-Riemannian cases in a unified way and obtain some algebraic...

- Properties of 2-dimensional time-like ruled surfaces in the Minkowski space Rn1. Tosun, Murat; Aydemir, Ismail; Kuruoglu, Nuri // Proceedings of the Estonian Academy of Sciences, Physics, Mathem;Dec2005, Vol. 54 Issue 4, p235
Some results, which are well known for the ruled surfaces in the Euclidean space Rnare generalized here to the case of Rn1In particular, it is shown that a time-like ruled surface in Rn1is developable if and only if it has zero Gaussian curvature; moreover, it is then minimal if and only if it...

- Spectral flow and iteration of closed semi-Riemannian geodesics. Javaloyes, Miguel; Piccione, Paolo // Calculus of Variations & Partial Differential Equations;Dec2008, Vol. 33 Issue 4, p439
We introduce the notion of spectral flow along a periodic semi-Riemannian geodesic, as a suitable substitute of the Morse index in the Riemannian case. We study the growth of the spectral flow along a closed geodesic under iteration, determining its asymptotic behavior.