We extend Prekopa's Theorem and the Brunn-Minkowski Theorem from convexity to F-subharmonicity. We apply this to the interpolation problem of convex functions and convex sets introducing a new notion ...of “harmonic interpolation” that we view as a generalization of Minkowski-addition.
In the planar setting, the Radó–Kneser–Choquet theorem states that a harmonic map from the unit disk onto a Jordan domain bounded by a convex curve is a diffeomorphism provided that the boundary ...mapping is a homeomorphism. We prove the injectivity criterion of Radó–Kneser–Choquet for $p$-harmonic mappings between Riemannian surfaces. In our proof of the injectivity criterion we approximate the $p$-harmonic map with auxiliary mappings that solve uniformly elliptic systems. We prove that each auxiliary mapping has a positive Jacobian by a homotopy argument. We keep the maps injective all the way through the homotopy with the help of the minimum principle for a certain subharmonic expression that is related to the Jacobian.
In this paper we calculate the norm of the bounded composition operator on the Fock space over
. This verifies a conjecture posed in Carswell B, MacCluer B, Schuster A. Composition operators on the ...Fock space. Acta Sci Math (Szeged). 2003;69:871-887.
In this note subharmonic and plurisubharmonic functions on a complex space are studied intrinsically. For applications subharmonicity is characterized more effectually in terms of properties that ...need be verified only locally off a thin analytic subset; these include the submean-value inequalities, the spherical (respectively, solid) monotonicity, near as well as weak subharmonicity. Several results of Gunning 9, K and L are extendable via regularity to complex spaces. In particular, plurisubharmonicity amounts (on a normal space) essentially to regularized weak plurisubharmonicity, and similarly for subharmonicity (on a general space). A generalized Hartogs’ lemma and constancy criteria for certain matrix-valued mappings are given.
The model of free charged Bosons in an external constant magnetic field inside a cylinder, one of the few locally gauge covariant systems amenable to analytic treatment, is rigorously investigated in ...the semiclassical approximation. The model was first studied by Schafroth and is suitable for the description of quasi-bound electron pairs localized in physical space, the so-called Schafroth pairs, which occur in certain compounds. Under the assumption of existence of a solution of the semiclassical problem for which the ground state (g.s.) expectation value of the current
<
j
→
(
x
→
)
>
is of the London form, i.e.,
<
j
→
(
x
→
)
>
=
-
c
|
ϕ
0
(
x
→
)
|
2
A
→
(
x
→
)
, where c is a positive constant,
A
→
the vector potential and
ϕ
0
the one-particle g.s. wave function, as well as some regularity assumptions, the magnetic induction may be proved to decay exponentially from its value on the surface of the cylinder. An important role is played by a theorem on the pointwise monotonicity of the ground state wave function on the potential.
This paper is devoted to the comparison of various shape properties of triangular Bézier surfaces and of their Bézier nets, such as polyhedral convexity, axial convexity and subharmonicity. In order ...to better compare these properties, the different notations used by different authors are unified. It also includes counterexamples for the results that are not true.
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