Consejo Nacional de Ciencia y Tecnología (Mexico)

In this paper, we first establish the localization of the Bergman kernels for unbounded pseudoconvex domains near a D'Angelo finite type boundary point. This result was proved by Engliš more than twenty years ago for bounded pseudoconvex domains and had remained open in the unbounded setting. Closely related earlier results of this kind were obtained by Fefferman, Kerzman, Boutet de Monvel-Sjöstrand, Boas, Bell, etc. A recent work by Ebenfelt, Xiao, and Xu contains, among other things, a related theorem to this problem for the unit disk bundle of a negatively curved holomorphic line bundle over a Kähler manifold which is not a domain in a complex Euclidean space. Using the localization theorem together with an extension theorem of Mir-Zaitsev, we show that the Bergman metric of a bounded pseudoconvex domain with real-analytic boundary is Einstein if and only if the domain is biholomorphic to the unit ball, thus contributing to an old conjecture of Cheng-Yau. A crucial step in the proof is to show that the Bergman metric of a smooth (possibly unbounded) pseudoconvex domain cannot be Kähler-Einstein when the boundary contains a non-strongly pseudoconvex h-extendible point. Then we show that a bounded weakly pseudoconvex real analytic domain whose Bergman metric is Kähler-Einstein has a weakly pseudoconvex h-extendible boundary point and thus reduces the study to the h-extendible case.

In [CCHT25], the authors introduced multiple Eisenstein series of arbitrary rank in positive characteristic and the q-shuffle algebra ℰ associated with them. In the present paper, we establish a class of linear independence results for multiple Eisenstein series. We also prove that the q-shuffle algebra ℛ of multiple zeta values embeds into the inverse limit of the spaces of multiple Eisenstein series with respect to the rank r, and that ℰ is isomorphic to the tensor square of ℛ. As an application, we show that ℰ is an associative algebra, thereby verifying the conjecture proposed in [CCHT25]

We construct infinite-time singularities with vanishing mean curvature for Lagrangian mean curvature flow in Gibbons–Hawking spaces. We consider circle-invariant Lagrangian 2-spheres whose quotient curves are concave and are C^2-close to a collection of consecutive collinear segments. We prove that the corresponding flow exists smoothly for all time and converges to the associated A_n-1-chain of special Lagrangian spheres. Although the mean curvature converges uniformly to zero, the second fundamental form becomes unbounded. More precisely, logmax |A( · ,t)| is comparable to √(t) as t→∞. The proof is based on a one-parameter family of barrier curves and a detailed analysis of their asymptotics. In this way, we refine the infinite-time convergence picture arising in the work of Lotay and Oliveira by proving curvature blow-up and estimating its rate in this semi-stable case.

We introduce an evolving-plane ansatz for the explicit construction of entire minimal graphs of dimension n ( n≥ 3 ) and codimension m ( m≥ 2 ). Under this ansatz, the minimal surface system reduces to the geodesic equation on the Grassmannian in affine coordinates. Geometrically, this equation dictates how the slope of an (n-1) plane evolves as it sweeps out a minimal graph. This framework yields a large family of explicit entire minimal graphs of arbitrary dimension n and arbitrary codimension m. For each entire minimal graph, its conormal bundle gives rise to an entire special Lagrangian graph in ℂ^n+m .

El concepto de sinhogarismo continúa asociado fundamentalmente a vivir en situación de calle, circunstancia experimentada principalmente por hombres, lo que tiene como consecuencia que ciertas condiciones de acomodo residencial de las mujeres queden en la sombra. Su menor participación en el mercado de trabajo, en sectores informales y de menor remuneración, aunada a condiciones de desigualdad de género, estatus migratorio u origen nacional, deriva en un sinhogarismo femenino invisibilizado. En este análisis se busca mostrar el fenómeno del sinhogarismo oculto en mujeres migrantes venezolanas residentes en Colombia a partir de tres elementos: la accesibilidad, la asequibilidad y la habitabilidad de la vivienda. Con ese propósito se emplea un análisis multimétodo que posibilita dar cuenta de dicho problema en ese país utilizando tanto fuentes cuantitativas como cualitativas. Para el análisis cuantitativo se usan datos de la Gran Encuesta Integrada de Hogares, 2024, y para la aproximación cualitativa se recuperan los relatos obtenidos en entrevistas realizadas a 21 mujeres migrantes venezolanas residentes en Bogotá. A partir del análisis de datos se evidencia que las mujeres migrantes experimentan condiciones de sinhogarismo, el cual es invisibilizado debido a las estrategias empleadas por ellas para su acomodo residencial.