In this paper we are concerned with the convergence of solutions of elliptic and analytic Monge-Ampère equations. Theorem 1 gives the principal result of this paper. The example on p.^372 indicates the possibility of certain types of singularities which for linear elliptic equations cannot occur. Theorems 2 and 3 give sufficient conditions for the analyticity of the limit function. These condit...

Extending DiNezza-Lu's approach to the setting of big cohomology classes, we prove that solutions degenerate complex Monge-Amp{\`e}re equations on compact K{\"a}hler manifolds are continuous a Zariski open set. This allows us show singular K{\"a}hler-Einstein metrics log canonical varieties general type have potentials ample locus outside non-klt part.

Nowadays, estimating the ampere consumption and achieve to the optimum condition from the perspective of energy consumption is one of the most important steps to reduce the production costs. In this research it is tried to develop an accurate model for estimating the ampere consumption by using the artificial neural networks (ANN).In the first step, experimental studies were carried out on 7 ca...

We define Chern and Segre forms, or rather currents, associated with a Griffiths positive singular hermitian metric $h$ analytic singularities on holomorphic vector bundle $E$. The currents are constructed as pushforwards of generalized Monge-Amp\`ere products the projectivization represent classes $E$, respectively, coincide forms $E$ $h$, where is smooth. Moreover, our by first three authors ...

Optimal mass transportation can be traced back to Gaspard Monge’s famous paper of 1781: ‘Mémoire sur la théorie des déblais et des remblais’. The problem there is to minimize the cost of transporting a given distribution of mass from one location to another. Since then, it has become a classical subject in probability theory, economics and optimization. At the end of the 80’s, the seminal work ...

<p style='text-indent:20px;'>By constructing explicit supersolutions, we obtain the optimal global Hölder regularity for several singular Monge-Ampère equations on general bounded open convex domains including those related to complete affine hyperbolic spheres, and proper hyperspheres. Our analysis reveals that certain singular-looking equations, such as <inline-formula><tex-mat...

Using Monge-Amp\`ere geometry, we study the singular structure of a class nonlinear equations in three dimensions, arising geophysical fluid dynamics. We extend seminal earlier work on geometry by examining role an induced metric Lagrangian submanifolds cotangent bundle. In particular, show that signature serves as classification equation, while singularities and elliptic-hyperbolic transitions...

A Bäcklund transformation between two hyperbolic Monge-Am-p` ere systems may be described as a certain type of exterior differential system on a 6-dimensional manifold B. The transformation is homogeneous if the group of symmetries of the system acts transitively on B. We give a complete classification of homogeneous Bäcklund transformations between hyperbolic Monge-Ampère systems.