Related papers: The extremal plurisubharmonic function of the toru…

We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…

Extremal length is an important conformal invariant on Riemann surface. It is closely related to the geometry of Teichmuller metric on Teichmuller space. By identifying extremal length functions with energy of harmonic maps from Riemann…

We prove that any embedded Maslov index two analytic disc attached to a totally real torus in the complex two-dimensional affine space extends to an analytic filling provided that the torus is contained in a regular level set of a strictly…

We systematically produce algebraic varieties with torus action by constructing them as suitably embedded subvarieties of toric varieties. The resulting varieties admit an explicit treatment in terms of toric geometry and graded ring…

We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in…

We prove some results which give sufficient conditions so that pointwise approximation of negative plurisubharmonic functions on complex varieties by continuous plurisubharmonic ones is possible.

We study a disc formula for the relative extremal function for Borel sets in complex manifolds.

The maximally compact representation of a regular orbit is in terms of its action-angle variables. Computing the map between a trajectory's Cartesian coordinates and its action-angle variables is called torus construction. This article…

We establish plurisubharmonicity of the envelope of Lelong functional on almost complex manifolds of real dimension four, thereby we generalize the corresponding result for complex manifolds.

We prove that the maximum of two smooth strictly plurisubharmonic functions on an almost complex manifold can be uniformly approximated by smooth strictly plurisubharmonic functions.

In this paper, we investigate the extremal functions for anisotropic Trudinger-Moser inequalities. Our method uses convex symmetrization, the continuity of the supremum function, together with the relation between the supremums of the…

We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…

We consider a class $\THO$ of typically real harmonic functions on the unit disk that contains the class of normalized analytic and typically real functions. We also obtain some partial results about the region of univalence for this class.

We calculate the Fourier transform of a spherically symmetric exponential function. Our evaluation is much simpler than the known one. We use the polar coordinates and reduce the Fourier transform to the integral of a rational function of…

Tropicalization is a procedure that assigns polyhedral complexes to algebraic subvarieties of a torus. If one fixes a weighted polyhedral complex, one may study the set of all subvarieties of a toric variety that have that complex as their…

``Quasi-elliptic'' functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated. A related structure has appeared…

Topological characterization of torus groups is given.

The efficacy of using complexifications to understand the structure of real algebraic groups is demonstrated. In particular the following results are proved: a) If L is an algebraic subgroup of a connected real algebraic group G such that…

We use our disc formula for the Siciak-Zahariuta extremal function to characterize the polynomial hull of a connected compact subset of complex affine space in terms of analytic discs.

A variant of Siu's analyticity theorem is proved for relative types of plurisubharmonic functions. Some results on propagation of plurisubharmonic singularities and maximality of pluricomplex Green functions with analytic singularities are…