In differential geometry and topology one often deals with systems of partial differential equations, as well as partial differential inequalities, that have infinitely many solutions whatever boundary conditions are imposed. It was discovered in the fifties that the solvability…
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The principal aim of this research is to establish certain formulas for the homology classes represented by the self-intersection loci of an immersed submanifold. This paper provides a generalization of a formula for higher order intersection multiplicities.
We prove that the singular set of a harmonic map from a smooth Riemannian domain to a Riemannian DM-complex is of Hausdorff codimension at least two. We also explore monotonicity formulas and an order gap theorem for approximately harmonic maps. These regularity results have app…
