A complement to the Fredholm theory of elliptic systems on bounded domains.
A complete differential formalism for stochastic calculus in manifolds
A computation of the equivariant index of the Dirac operator
A conformally invariant sphere theorem in four dimensions
A construction of non-flat non-homogeneous symmetric parabolic geometries
We construct series of examples of non-flat non-homogeneous parabolic geometries that carry a symmetry of the parabolic geometry at each point.
A convergence result for finite volume schemes on Riemannian manifolds
This paper studies a family of finite volume schemes for the hyperbolic scalar conservation law on a closed Riemannian manifold M. For an initial value in BV(M) we will show that these schemes converge with a convergence rate towards the entropy solution. When M is 1-dimensional the schemes are TVD and we will show that this improves the convergence rate to
A counterexample for the optimality of Kendall-Cranston coupling.
A counterexample to smooth leafwise Hodge decomposition for general foliations and to a type of dynamical trace formulas
We construct a two dimensional foliation with dense leaves on the Heisenberg nilmanifold for which smooth leafwise Hodge decomposition does not hold. It is also shown that a certain type of dynamical trace formulas relating periodic orbits with traces on leafwise cohomologies does not hold for arbitrary flows.
A differentiable isomorphism between Wiener space and path group
A Direct Approach to the Determination of Gaussian and Scalar Curvature Functions.
A directional compactification of the complex Bloch variety.
A directional compactification of the complex Fermi surface
A discreteness criterion for the spectrum of the Laplace--Beltrami operator on quasimodel manifolds.
A double complex related with a system of partial differential equations. II
A double complex related with a system of partial differential equations. I
A few symmetry results for nonlinear elliptic PDE on noncompact manifolds
A fixed point formula of Lefschetz type in Arakelov geometry II: A residue formula
This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result of the first paper to prove a residue formula "à la Bott" for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable torus; recent results of Bismut- Goette on the equivariant (Ray-Singer) analytic torsion play a key role in the proof.
A fully nonlinear version of the Yamabe problem on manifolds with boundary
We propose to study a fully nonlinear version of the Yamabe problem on manifolds with boundary. The boundary condition for the conformal metric is the mean curvature. We establish some Liouville type theorems and Harnack type inequalities.
A Fundamental Property of Monge Characteristics in Involutive Systems of Non-Linear Partial Differential Equations and its Application.
A general class of Gevrey-type pseudo differential operators