The index of transversally elliptic complexes
The Induced Connections on the Subspaces in Miron's Osckm
The infinite Brownian loop on a symmetric space.
The information metric on rational maps.
The ..-invariant of hyperbolic 3-manifolds.
The inverse problem in the calculus of variations: new developments
We deal with the problem of determining the existence and uniqueness of Lagrangians for systems of second order ordinary differential equations. A number of recent theorems are presented, using exterior differential systems theory (EDS). In particular, we indicate how to generalise Jesse Douglas’s famous solution for . We then examine a new class of solutions in arbitrary dimension and give some non-trivial examples in dimension 3.
The iterated version of a translative integral formula for sets of positive reach
By taking into account the work of J. Rataj and M. Zähle [Geom. Dedicata 57, 259-283 (1995; Zbl 0844.53050)], R. Schneider and W. Weil [Math. Nachr. 129, 67-80 (1986; Zbl 0602.52003)], W. Weil [Math. Z. 205, 531-549 (1990; Zbl 0705.52006)], an integral formula is obtained here by using the technique of rectifiable currents.This is an iterated version of the principal kinematic formula for sets of positive reach and generalized curvature measures.
The Jacobi fields for a spray on the tangent bundle.
The jet prolongations of -fibred manifolds and the flow operator
Let , , , , be natural numbers such that . We prove that any --natural operator transforming -projectable vector fields on -dimensional -fibred manifolds into vector fields on the -jet prolongation bundle is a constant multiple of the flow operator .
The Kashiwara cojugation and wave-front sets of regular holonomic distributions on a complex manifold.
The Kashiwara conjugation and wave-front sets of regular holonomic distributions on a complex manifold (Erratum).
The metric in gauge theory: an introduction and some applications
We discuss the geometry of the Yang-Mills configuration spaces and moduli spaces with respect to the metric. We also consider an application to a de Rham-theoretic version of Donaldson’s μ-map.
The L2-Structure of Moduli spaces of Einstein Metrics on 4-Manifolds.
The Lagrange complex
The Lagrange Intersections for (CPn, RPn).
The Landau-Lifshitz equation with the external field - a new extension for harmonic maps with values in S2.
The Laplace operator on a hyperbolic manifold. II. Eisenstein series and the scattering matrix.
The Laplace operator on hyperbolic three manifolds with cusps of non-maximal rank.
The Laplace spectrum and Hermitian spaces.
The Laplace-Beltrami operator in almost-Riemannian Geometry
We study the Laplace-Beltrami operator of generalized Riemannian structures on orientable surfaces for which a local orthonormal frame is given by a pair of vector fields that can become collinear.Under the assumption that the structure is 2-step Lie bracket generating, we prove that the Laplace-Beltrami operator is essentially self-adjoint and has discrete spectrum. As a consequence, a quantum particle cannot cross the singular set (i.e., the set where the vector fields become collinear) and the...