Takeshi Isobe

Topological and analytical properties of Sobolev bundles. II. Higher dimensional cases

We define various classes of Sobolev bundles and connections and study their topological and analytical properties. We show that certain kinds of topologies (which depend on the classes) are well-defined for such bundles and they are stable with respect to the natural Sobolev topologies. We also extend the classical Chern-Weil theory for such classes of bundles and connections. Applications related to variational problems for the Yang-Mills functional are also given.

A regularity result for a class of degenerate Yang-Mills connections in critical dimensions

Abstract We show that any weak solution to the p-Yang-Mills equations of Sobolev class W 1,p defined on an m-dimensional manifold is W 2,p -gauge equivalent to a C 1,δ -connection for some 0 < δ < 1 provided p ≥ m/2.

Energy estimate, energy gap phenomenon, and relaxed energy for Yang-Mills functional

Concerning the Yang-Mills functional overR5 ∖ {a1,...,ap},we calculate its energy using geometrical term. Moreover, we may find the energy gap phenomenon with respect to the Yang-Mills energy which occurs also for harmonic mapping etc. From this, we propose to consider new functional, called relaxed energy.

Obstructions to the extension problem of Sobolev mappings

Let

Regularity of harmonic maps into a static Lorentzian manifold

M

Non-existence and uniqueness results for boundary value problems for Yang-Mills connections

and

ON A MINIMIZING PROPERTY OF THE HOPF SOLITON IN THE FADDEEV–SKYRME MODEL

N

Nonlinear Dirac equations with critical nonlinearities on compact spin manifolds

be compact manifolds with

Existence results for solutions to nonlinear Dirac equations on compact spin manifolds

\partial M\ne\emptyset

On the existence of nonlinear Dirac-geodesics on compact manifolds

. We show that when