1,520 research outputs found
Continuity of Monge-Amp\`ere Potentials with Prescribed Singularities
No full textWe study the continuity of solutions to complex Monge-Ampere equations with
prescribed singularities. This generalizes the previous results of DiNezza-Lu
and the author. As an application, we can run the Monge-Ampere flow starting at
a current with prescribed singularities.Comment: accepted version in J. Geom. Ana
The Obstacle Problem for Monge-Ampère Equation
No full textWe consider the obstacle problem for the degenerated Monge-Ampère equation. We prove the existence of the greatest viscosity sub-solution,and the C 1;1 -regularity. Then the solution satisfies the concave uniformly elliptic equation. We use the author's previous work to show the C 1;ff -regularity of the free boundary. Finally, we discuss the stability of the free boundary
On a mixed Monge-Ampere operator for quasiplurisubharmonic functions with analytic singularities
No full textWe consider mixed Monge-Ampere products of quasiplurisubharmonic functions with analytic singularities, and show that such products may be regularized as explicit one-parameter limits of mixed Monge-Ampere products of smooth functions, generalizing results of Andersson, Blocki and the last author in the case of non-mixed Monge-Ampere products. Connections to the theory of residue currents, going back to Coleff-Herrera, Passare and others, play an important role in the proof. As a consequence we get an approximation of Chern and Segre currents of certain singular hermitian metrics on vector bundles by smooth forms in the corresponding Chern and Segre classes
Boundedness of maximal function related to the Monge–Ampère equation
No full textAbstractIn this paper, we establish the boundedness of maximal function on Morrey spaces related to the Monge–Ampère equation
Lecture notes on generalized Monge-Amp\`ere equations and subvarieties
No full textThese are the lecture notes for the Morningside Center of Mathematics
Geometry Summer School on August 15-20, 2022. These lectures sketch the results
by Yau, Demailly-Paun, the author, and Datar-Pingali about generalized
Monge-Amp\`ere equations and subvarieties and aim to use these results to study
the Hodge conjecture
Geometry of complex Monge-Ampere equations
No full textIn this thesis, we study three problems related to Complex Monge-Amp`ere equations. After the introduction and preliminary, In chapter 3, we study K ̈ahler Ricci flow on Fano bundle, with finite time singularity. we show that under the suitable assumption on the initial and ending K ̈ahler class, the evolving K ̈ahler metrics along K ̈ahler Ricci flow have uniform diameter bound and moreover, if we assume the fiber of Fano bundle is Pn or Mm,k, the evolving metric will converge to a K ̈ahler metric on the base of the Fano bundle in Gromov-Hausdorff sense, which generalizes the result of Song-Szekelyhidi- Weinkove [103] who study the K ̈ahler Ricci flow on projective bundle.
In chapter 4, based on Kolodziej’s fundamental result on C0 estimate of complex Monge-Amp`ere equation, we study the geometric property of complex manifolds cou- pled with a family of K ̈ahler metrics which come from solutions of a family of complex Monge-Amp`ere equations. As a application, on a minimal K ̈ahler manifold with inter- mediate Kodaira dimension, we obtain uniform diameter bound of a family of collapsing K ̈ahler metrics whose K ̈ahler class is small perturbation of the canonical class. This is our first attempt to understand canonical metric on complex manifold with nef canon- ical class.
In chapter 5, we further study degeneration of K ̈ahler-Einstein metrics with negative curvature on canonical polarized complex manifold. For this purpose, we construct complete K ̈ahler-Einstein metric near isolated log canonical singularity through two different methods and for those log canonical singularity coupled with a model metric satisfying bounded geometry property roughly, we prove a rigidity result concerning complete K ̈ahler-Einsteins near the singularity.Ph.D.Includes bibliographical reference
Las diversas entonaciones de una sola voz. Historia, ciudadanía y nación en Carlos Monge Alfaro
No full textAn analysis is presented of the work the historian Carlos Monge Alfaro and of the different ways that he narrates the construction of history from a theoretical perspective and the experience of the Costa Rican world. Monge Alfaro is conceived as an author who presents contradictory views of the social universe and not as a coherent and apprehensible intellectual, constructing ideas which are linked in his different texts. When Monge Alfaro stopped being an intellectual of the opposition to participate in the construction of a hegemonic project, he reconstructed his initial discourse as a response to the transformations present in his conception of the relation between the social world and power.Analiza la obra del historiador Carlos Monge Alfaro y explora sus diferentes narrativas de la construcción de la historia desde la perspectiva teórica y de la experiencia del mundo costarricense. Concibe a Monge Alfaro como un autor que ensaya visiones contrapuestas del universo social, y no como un intelectual coherente y aprehensible, constructor de ideas claramente hilvanadas en sus diferentes textos. Cuando Monge Alfaro deja de ser un intelectual de oposición para participar en la construcción de un proyecto hegemónico, reconstituye su discursividad inicial en respuesta a las transformaciones dadas en su concepción de la relación entre el mundo social y el poder
Las diversas entonaciones de una sola voz. Historia, ciudadanía y nación en Carlos Monge Alfaro
No full textAnaliza la obra del historiador Carlos Monge Alfaro y explora sus diferentes narrativas de la construcción de la historia desde la perspectiva teórica y de la experiencia del mundo costarricense. Concibe a Monge Alfaro como un autor que ensaya visiones contrapuestas del universo social, y no como un intelectual coherente y aprehensible, constructor de ideas claramente hilvanadas en sus diferentes textos. Cuando Monge Alfaro deja de ser un intelectual de oposición para participar en la construcción de un proyecto hegemónico, reconstituye su discursividad inicial en respuesta a las transformaciones dadas en su concepción de la relación entre el mundo social y el poder. An analysis is presented of the work the historian Carlos Monge Alfaro and of the different ways that he narrates the construction of history from a theoretical perspective and the experience of the Costa Rican world. Monge Alfaro is conceived as an author who presents contradictory views of the social universe and not as a coherent and apprehensible intellectual, constructing ideas which are linked in his different texts. When Monge Alfaro stopped being an intellectual of the opposition to participate in the construction of a hegemonic project, he reconstructed his initial discourse as a response to the transformations present in his conception of the relation between the social world and power
Une approche itérative au problème des valeurs propres pour l'opérateur de Monge-Ampère complexe
No full textInternational audienceWe present an iterative approach to approximate the solution to the Dirichlet complex Monge-Ampère eigenvalue problem on a bounded strictly pseudoconvex domain in C^n . This approach is inspired by a similar approach initiated by F. Abedin, J. Kitagawa who considered the real Monge-Ampère operator on a strictly convex domain in R N .This work is based on recent results obtained by P. Badiane and the author on the existence and uniqueness of the solution to the Dirichlet eigenvalue problem for the complex Monge-Ampère operator.However, the iterative approach does not require the a priori knowledge of the first eigenvalue but it provides an effective scheme for approximating it, as well as the associated eigenfunction.Nous présentons une approche itérative pour approximer la solution du problème aux valeurs propres de l'opérateur de Monge-Ampère complexe sur un domaine strictement pseudo-convexe borné en C^n . Cette approche s'inspire d'une approche similaire initiée par F. Abedin et J. Kitagawa qui ont considéré l'opérateur de Monge-Ampère réel sur un domaine strictement convexe en R^N .Ce travail s'appuie sur les résultats récents obtenus par P. Badiane et l'auteur sur l'existence et l'unicité de la solution du problème aux valeurs propres de Monge-Ampère complexe de Dirichlet.Cependant, l'approche itérative ne nécessite pas la connaissance a priori de la première valeur propre, mais elle fournit un schéma efficace pour l'approximer, ainsi que la fonction propre associée.</div
Las diversas entonaciones de una sola voz. Historia, ciudadanía y nación en Carlos Monge Alfaro
No full textAnaliza la obra del historiador Carlos Monge Alfaro y explora sus diferentes narrativas de la construcción de la historia desde la perspectiva teórica y de la experiencia del mundo costarricense. Concibe a Monge Alfaro como un autor que ensaya visiones contrapuestas del universo social, y no como un intelectual coherente y aprehensible, constructor de ideas claramente hilvanadas en sus diferentes textos. Cuando Monge Alfaro deja de ser un intelectual de oposición para participar en la construcción de un proyecto hegemónico, reconstituye su discursividad inicial en respuesta a las transformaciones dadas en su concepción de la relación entre el mundo social y el poder.
An analysis is presented of the work the historian Carlos Monge Alfaro and of the different ways that he narrates the construction of history from a theoretical perspective and the experience of the Costa Rican world. Monge Alfaro is conceived as an author who presents contradictory views of the social universe and not as a coherent and apprehensible intellectual, constructing ideas which are linked in his different texts. When Monge Alfaro stopped being an intellectual of the opposition to participate in the construction of a hegemonic project, he reconstructed his initial discourse as a response to the transformations present in his conception of the relation between the social world and power
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