Related papers: Extremal metrics on toric surfaces, I
We introduce a surface finite element method for the numerical solution of Navier-Stokes equations on evolving surfaces with a prescribed deformation of the surface in normal direction. The method is based on approaches for the full surface…
In this article a new upper bounds for the multiple trigonometrical integrals are found. The method of the work based on a new method of estimation for the areas of algebraic surfaces.
In this paper we prove the existence and regularity of solutions to the first boundary value problem for Abreu's equation, which is a fourth order nonlinear partial differential equation closely related to the Monge-Ampere equation. The…
We construct extremal metrics on the total space of certain destabilising test configurations for strictly semistable K\"ahler manifolds. This produces infinitely many new examples of manifolds admitting extremal K\"ahler metrics. It also…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
This paper completes a programme to determine which toric surfaces admit Kahler metrics of constant scalar curvature/
In this paper, we propose an approach for solving PDEs on evolving surfaces using a combination of the trace finite element method and a fast marching method. The numerical approach is based on the Eulerian description of the surface…
In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving surface we use parametric finite elements of degree $\ell…
In this paper we introduce higher extremal Kahler metrics. We provide an example of the same on a minimal ruled surface. We also prove a perturbation result that implies that there are non-trivial examples of higher constant scalar…
We study a generalized Abreu equation and derive some estimates.
In this short note, we study the smoothness of the extremal solutions to the Liouville system
We are concerned with a Liouville-type equation with exponential nonlinearities on a compact surface which describes the mean field equation of the equilibrium turbulence with arbitrarily signed vortices. We provide the first multiplicity…
The paper is devoted to some extremal problems, related to convex polygons in the Euclidean plane and their perimeters. We present a number of results that have simple formulations, but rather intricate proofs. Related and still unsolved…
In this paper we prove the interior regularity for the solution to the Abreu equation in any dimension assuming the existence of the $C^0$ estimate.
Singular fourth-order Abreu equations have been used to approximate minimizers of convex functionals subject to a convexity constraint in dimensions higher than or equal to two. For Abreu type equations, they often exhibit different…
We generalize the bifurcation technique of Bando-Mabuchi in the context of extremal metrics.
A general method to derive the master equations for extremal models is established. These systems are shown to develop a peculiar kind of correlations between elements related to the characterization of extremal dynamics as an information…
We develop a constructive process which determines all extreme points of the unit ball of the space of $m$--linear forms, $m\geq1.$ Our method provides a full characterization of the geometry of that space through finitely many elementary…
In this paper, we concern trace Trudinger-Moser inequalities on a compact Riemann surface with smooth boundary. This kind of inequalities were extensively studied by Osgood-Phillips-Sarnak [24], Liu [20], Li-Liu [17], Yang [31, 32] and…
In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the convex case. Then we apply this machinery to deriving new…