Higher Equivariant Index Theorem for Homogeneous spaces.
Higher -indices and applications
Higher index theorems and the boundary map in cyclic cohomology.
Higher order absolute differentiation with respect to generalized connections
Higher order Cartan connections.
Higher order Cartan connections
A Cartan connection associated with a pair is defined in the usual manner except that only the injectivity of is required. For an -th order connection associated with a bundle morphism the concept of Cartan order is defined, which for , and coincides with the classical definition. Results are obtained concerning the Cartan order of -th order connections that are the product of first order (Cartan) connections.
Higher order connections.
Higher order geodesic symmetries
Higher order graded and berezinian lagrangian densities and their Euler-Lagrange equations
Higher order Grassmann fibrations and the calculus of variations.
Higher order jet involution
We introduce an exchange natural isomorphism between iterated higher order jet functors depending on a classical linear connection on the base manifold. As an application we study the prolongation of higher order connections to jet bundles.
Higher order linear connections from first order ones
We describe how find all -natural operators transforming torsion free classical linear connections on -manifolds into -th order linear connections on .
Higher order torsions of manifolds with connection
Higher order valued reduction theorems for classical connections
We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the 2nd order valued reduction theorems we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection.
Higher symmetries of the Laplacian via quantization
We develop a new approach, based on quantization methods, to study higher symmetries of invariant differential operators. We focus here on conformally invariant powers of the Laplacian over a conformally flat manifold and recover results of Eastwood, Leistner, Gover and Šilhan. In particular, conformally equivariant quantization establishes a correspondence between the algebra of Hamiltonian symmetries of the null geodesic flow and the algebra of higher symmetries of the conformal Laplacian. Combined...
Higher-order phase transitions with line-tension effect
The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of the liquid. This problem, also known as the liquid-drop problem, was studied by Modica in [Ann. Inst. Henri Poincaré, Anal. non linéaire 4 (1987) 487–512], and in a different form by Alberti et al. in [Arch. Rational Mech. Anal.u is a scalar density function and...
Higher-order phase transitions with line-tension effect
The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of the liquid. This problem, also known as the liquid-drop problem, was studied by Modica in [Ann. Inst. Henri Poincaré, Anal. non linéaire4 (1987) 487–512], and in a different form by Alberti et al. in [Arch. Rational Mech. Anal.144 (1998) 1–46] for a first-order...
Higher-order preconnections in synthetic differential geometry of jet bundles.
Hitchin' s self-duality equations on complete Riemannian manifolds.
Hodge theory for twisted differentials
We study cohomologies and Hodge theory for complex manifolds with twisted differentials. In particular, we get another cohomological obstruction for manifolds in class C of Fujiki. We give a Hodgetheoretical proof of the characterization of solvmanifolds in class C of Fujiki, first stated by D. Arapura.