A Variational Proof of the Gauss-Bonnet Formula.
A variational solution of the A. D. Aleksandrov problem of existence of a convex polytope with prescribed Gauss curvature
In his book on convex polytopes [2] A. D. Aleksandrov raised a general question of finding variational formulations and solutions to geometric problems of existence of convex polytopes in , n ≥ 2, with prescribed geometric data. Examples of such problems for closed convex polytopes for which variational solutions are known are the celebrated Minkowski problem [2] and the Gauss curvature problem [20]. In this paper we give a simple variational proof of existence for the A. D. Aleksandrov problem...
A vector lattice variant of the ergodic theorem
A volume comparison estimate with radially symmetric Ricci curvature lower bound and its applications.
A volume comparison theorem and number of ends for manifolds with asymptotically nonnegative Ricci curvature.
In this paper we establish a volume comparison theorem for cocentric metric balls at arbitrary point for manifolds with asymptotically nonnegative Ricci curvature, which will allow us to prove the finiteness of the number of ends.
A Weierstrass-Kenmotsu formula for prescribed mean curvature surfaces in hyperbolic space
A Weierstrass-type representation for harmonic maps from Riemann surfaces to general Lie groups.
A Weitzenbôck formula for the second fundamental form of a Riemannian foliation
Si considera la seconda forma fondamentale di foliazioni su varietà riemanniane e si ottiene una formula per il laplaciano - Se ne deducono alcune implicazioni per foliazioni su varietà a curvatura costante.
A xylophone detector in space
We discuss spacecraft Doppler tracking for detecting gravitational waves in which Doppler data recorded on the ground are linearly combined with Doppler measurements made on board a spacecraft. By using the four-link radio system first proposed by Vessot and Levine [1] we derive a new method for removing from the combined data the frequency fluctuations due to the Earth troposphere, ionosphere, and mechanical vibrations of the antenna on the ground. This method also reduces the frequency fluctuations...
A- субпланарные многообразия как вещественные реализации пространств над алгебрами
Abbildung der Flächen zweiten Grades nach Aehnlichkeit der Flächenelemente
Abelian analytic torsion and symplectic volume
This article studies the abelian analytic torsion on a closed, oriented, Sasakian three-manifold and identifies this quantity as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections. This identification computes the analytic torsion explicitly in terms of Seifert data.
Abelian complex structures on 6-dimensional compact nilmanifolds
We classify the -dimensional compact nilmanifolds that admit abelian complex structures, and for any such complex structure we describe the space of symplectic forms which are compatible with .
Abelian complex structures on solvable Lie algebras.
Abelian simply transitive affine groups of symplectic type
The set of all Abelian simply transitive subgroups of the affine group naturally corresponds to the set of real solutions of a system of algebraic equations. We classify all simply transitive subgroups of the symplectic affine group by constructing a model space for the corresponding variety of solutions. Similarly, we classify the complete global model spaces for flat special Kähler manifolds with a constant cubic form.
Abel's Theorem and Webs.
Abnormal sub-riemannian geodesics : Morse index and rigidity
Abnormality of trajectory in sub-Riemannian structure
In the sub-Riemannian framework, we give geometric necessary and sufficient conditions for the existence of abnormal extremals of the Maximum Principle. We give relations between abnormality, -rigidity and length minimizing. In particular, in the case of three dimensional manifolds we show that, if there exist abnormal extremals, generically, they are locally length minimizing and in the case of four dimensional manifolds we exhibit abnormal extremals which are not -rigid and which can be minimizing...
About a decomposition of the space of symmetric tensors of compact support on a Riemann manifold.
About almost symplectic structures on the total space of the tangent bundle.