This paper studies a family of nite volume schemes for the hyperbolic scalar conservation law ut +∇g · f(x, u) = 0 on a closed Riemannian manifold. For an initial value in BV(M) and an at most 2 -dimensional manifold we will show that these schemes converge with a h 1 4 convergence rate towards the entropy solution. When M is 1 -dimensional the schemes are TVD and we will show that this improve...

An L2 theory of differential forms is proposed for the Banach manifold of continuous paths on Riemannian manifolds M furnished with its Brownian motion measure. Differentiation must be restricted to certain Hilbert space directions, the H-tangent vectors. To obtain a closed exterior differential operator the relevant spaces of differential forms, the H-forms, are perturbed by the curvature of M...

If G is a compact Lie group and M a Riemannian G-manifold with principal orbits of codimension k then a section or canonical form for M is a closed, smooth k-dimensional submanifold of M which meets all orbits of M orthogonally. We discuss some of the remarkable properties of G-manifolds that admit sections, develop methods for constructing sections, and consider several applications. O. Introd...

The concept system around ‘quantity’ and ‘quantity value’ is fundamental for measurement science, but some very basic issues are still open on such concepts and their relations. This paper proposes a duality between quantities and quantity values, a proposal that simplifies their characterization and makes it consistent.

We obtain an estimate for the norm of the second fundamental form of stable H-surfaces in Riemannian 3-manifolds with bounded sectional curvature. Our estimate depends on the distance to the boundary of the surface and on the bound on the sectional curvature but not on the manifold itself. We give some applications, in particular we obtain an interior gradient estimate for H-sections in Killing...

Abstract. Let S be the group R ⋉ R endowed with the Riemannian symmetric space metric d and the right Haar measure ρ. The space (S, d, ρ) is a Lie group of exponential growth. In this paper we define an Hardy space H and a BMO space in this context. We prove that the functions in BMO satisfy the John–Nirenberg inequality and that BMO may be identified with the dual space of H. We then prove tha...

Riemannian vectorial collineations along with current Killing conservation are shown to lead to tensorial collineations for the energystress tensor in general relativity and in Einstein-Cartan Weyssenhoff fluid cosmology. PACS numbers : 0420,0450. Departamento de F́ısica Teórica Instituto de F́ısica UERJ Rua São Fco. Xavier 524, Rio de Janeiro, RJ Maracanã, CEP:20550-003 , Brasil. e-mail.: garcia...

We prove the long-standing Eckmann{Ruelle conjecture in dimension theory of smooth dynamical systems. We show that the pointwise dimension exists almost everywhere with respect to a compactly supported Borel probability measure with non-zero Lyapunov exponents, invariant under a C 1+ diieomorphism of a smooth Riemannian manifold. Let M be a smooth Riemannian manifold without boundary, and f : M...

Consider the sub-Riemannian Heisenberg group $\mathbb{H}$. In this paper, we answer following question: given a compact set $K \subseteq \mathbb{R}$ and continuous map $f\colon K \to \mathbb{H}$, when is there horizontal $C^m$ curve $F\colon \mathbb{R} \mathbb{H}$ such that $F|\_K = f$? Whitney originally answered question for real valued mappings, Fefferman provided complete functions defined ...