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Scattering matrix for asymptotically euclidean manifolds

Richard Melrose, Maciej Zworski (1994)

Journées équations aux dérivées partielles

Shapes of spheres of special nonholonomic left-invariant intrinsic metrics on some Lie groups.

Berestovskij, V.N., Zubareva, I.A. (2001)

Sibirskij Matematicheskij Zhurnal

Shells of monotone curves

Josef Mikeš, Karl Strambach (2015)

Czechoslovak Mathematical Journal

We determine in $ℝ^{n}$ the form of curves $C$ corresponding to strictly monotone functions as well as the components of affine connections $\nabla$ for which any image of $C$ under a compact-free group $Ω$ of affinities containing the translation group is a geodesic with respect to $\nabla$ . Special attention is paid to the case that $Ω$ contains many dilatations or that $C$ is a curve in $ℝ^{3}$ . If $C$ is a curve in $ℝ^{3}$ and $Ω$ is the translation group then we calculate not only the components of the curvature and the Weyl tensor but...

Simplicial nonpositive curvature

Tadeusz Januszkiewicz, Jacek Świątkowski (2006)

Publications Mathématiques de l'IHÉS

We introduce a family of conditions on a simplicial complex that we call local k-largeness (k≥6 is an integer). They are simply stated, combinatorial and easily checkable. One of our themes is that local 6-largeness is a good analogue of the non-positive curvature: locally 6-large spaces have many properties similar to non-positively curved ones. However, local 6-largeness neither implies nor is implied by non-positive curvature of the standard metric. One can think of these results as a higher...

Small eigenvalues of Riemann surfaces and graphs.

Marc Burger (1990)

Mathematische Zeitschrift

Smooth quasigroups and loops: forty-five years of incredible growth

Lev Vasilʹevich Sabinin (2000)

Commentationes Mathematicae Universitatis Carolinae

The remarkable development of the theory of smooth quasigroups is surveyed.

Some existence theorems for closed geodesics.

W. Ballmann, G. Thorbergsson (1983)

Commentarii mathematici Helvetici

Some isoperimetric inequalities and eigenvalue estimates

Christopher B. Croke (1980)

Annales scientifiques de l'École Normale Supérieure

Some properties of geodesic semi E-b-vex functions

Adem Kiliçman, Wedad Saleh (2015)

Open Mathematics

In this study, we introduce a new class of function called geodesic semi E-b-vex functions and generalized geodesic semi E-b-vex functions and discuss some of their properties.

Spectrum of a compact flat manifold.

Toshikazu Sunada (1978)

Commentarii mathematici Helvetici

Spectrum of the Laplace operator and periodic geodesics: thirty years after

Yves Colin de Verdière (2007)

Annales de l’institut Fourier

What is called the “Semi-classical trace formula” is a formula expressing the smoothed density of states of the Laplace operator on a compact Riemannian manifold in terms of the periodic geodesics. Mathematical derivation of such formulas were provided in the seventies by several authors. The main goal of this paper is to state the formula and to give a self-contained proof independent of the difficult use of the global calculus of Fourier Integral Operators. This proof is close in the spirit of...

Stability of the geodesic flow for the energy

Eric Boeckx, José Carmelo González-Dávila, Lieven Vanhecke (2002)

Commentationes Mathematicae Universitatis Carolinae

We study the stability of the geodesic flow $ξ$ as a critical point for the energy functional when the base space is a compact orientable quotient of a two-point homogeneous space.

Strongly geodesically automatic groups are hyperbolic.

P. Papasoglu (1995)

Inventiones mathematicae

Structure equations on generalized Finsler manifolds

Johanna Pék (2013)

Communications in Mathematics

In this paper we generalize the classical structure equations of Riemannian geometry to generalized Finsler manifolds.

Structure of geodesics in weakly symmetric Finsler metrics on H-type groups

Zdeněk Dušek (2020)

Archivum Mathematicum

Structure of geodesic graphs in special families of invariant weakly symmetric Finsler metrics on modified H-type groups is investigated. Geodesic graphs on modified H-type groups with the center of dimension $1$ or $2$ are constructed. The new patterns of algebraic complexity of geodesic graphs are observed.