A field equation defined by a Hurwitz pair
Biholomorphic invariance of capacity and the capacity of an annulus
A variational characterization of condenser capacities in within a class of plurisubharmonic functions
Foliations and the generalized complex Monge-Ampère equations
Foliations by complex manifolds involving the complex Hessian
SummaryIn 1979 the second named author proved, in a joint paper with J. Ławrynowicz, the existence of a foliation of a bounded domain in by complex submanifolds of codimension k+p-1, connected in some sense with a real (1,1) C³-form of rank k and the pth power of the complex Hessian of a C³-function u with im u plurisubharmonic and the property that for every leaf of this foliation the restricted functions im u, re u and , are pluriharmonic and holomorphic, respectively.Now the theorem is extended...
Only one of generalized gradients can be elliptic
Decomposing the space of k-tensors on a manifold M into the components invariant and irreducible under the action of GL(n) (or O(n) when M carries a Riemannian structure) one can define generalized gradients as differential operators obtained from a linear connection ∇ on M by restriction and projection to such components. We study the ellipticity of gradients defined in this way.
Weitzenböck Formula for SL(q)-foliations
A Weitzenböck formula for SL(q)-foliations is derived. Its linear part is a relative trace of the relative curvature operator acting on vector valued forms.
Weitzenböck Formula on Lie Algebroids
A Weitzenböck formula for the Laplace-Beltrami operator acting on differential forms on Lie algebroids is derived.
The global Yang-Mills equations depending on an arbitrary metric
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