Three spheres theorem for p-harmonic functions
Three spheres type theorem is proved for the p-harmonic functions defined on the complement of k-balls in the Euclidean n-dimensional space.
math.AP↗
arXiv subjects
Vladimir M. Miklyukov
Publications and source records attributed to Vladimir M. Miklyukov.
Stagnation zones for $\mathcal{A}$-harmonic functions on canonical domains
We study stagnation zones of $\mathcal{A}$-harmonic functions on canonical domains in the Euclidean $n$-dimensional space. Phragmen-Lindelöf type theorems are proved.
math.AP↗
Wiman and Arima theorems for quasiregular mappings
Generalizations of the theorems of Wiman and of Arima on entire functions are proved for spatial quasiregular mappings.
math.CA↗
Denjoy-Ahlfors Theorem for Harmonic Functions on Riemannian Manifolds and External Structure of Minimal Surfaces
We extend the well-known Denjoy-Ahlfors theorem on the number of different asymptotic tracts of holomorphic functions to subharmonic functions on arbitrary Riemannian manifolds. We obtain some new versions of the Liouville theorem for $\p$-harmonic functions without requiring the geodesic completeness requirement of a manifold. Moreover, an upper estimate of the topological index of the height function on a minimal surface in $\R{n}$ has been established and, as a consequence, a new proof of Bernstein's theorem on entire solutions has been derived. Other applications to minimal surfaces are also discussed.
math.DG↗
Ahlfors theorems for differential forms
Some counterparts of theorems of Phragmén-Lindelöf and of Ahlfors are proved for differential forms of ${\cal WT}$--classes.}
math.AP↗
On quasiplanes in Euclidean spaces
A variational inequality for the images of $k$-dimensional hyperplanes under quasiconformal maps of the $n$-dimensional Euclidean space is proved when $1\le k\le n-2 .$
math.CA↗