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pro vyhledávání: '"Alarcon, Antonio"'
Autor:
Alarcon, Antonio
We survey the recent history of the conformal Calabi-Yau problem consisting in determining the complex structures admitted by complete bounded minimal surfaces in $\mathbb{R}^3$. Moreover, we prove that for any minimally convex domain $\Omega$ in $\m
Externí odkaz:
http://arxiv.org/abs/2410.13687
Let $M$ be a Riemann surface biholomorphic to an affine algebraic curve. We show that the inclusion of the space $\Re \mathrm{NC}_*(M,\mathbb{C}^n)$ of real parts of nonflat proper algebraic null immersions $M\to\mathbb{C}^n$, $n\ge 3$, into the spac
Externí odkaz:
http://arxiv.org/abs/2406.04767
Autor:
Alarcon, Antonio, Larusson, Finnur
Let $M$ be an open Riemann surface and $A$ be the punctured cone in $\mathbb{C}^n\setminus\{0\}$ on a smooth projective variety $Y$ in $\mathbb{P}^{n-1}$. Recently, Runge approximation theorems with interpolation for holomorphic immersions $M\to\math
Externí odkaz:
http://arxiv.org/abs/2312.02795
Publikováno v:
Commun. Contemp. Math. (2024) 2450011
We prove that every open Riemann surface $M$ is the complex structure of a complete surface of constant mean curvature 1 (CMC-1) in the 3-dimensional hyperbolic space $\mathbb{H}^3$. We go further and establish a jet interpolation theorem for complet
Externí odkaz:
http://arxiv.org/abs/2306.14482
Autor:
Alarcon, Antonio, Forstneric, Franc
Publikováno v:
Mediterr. J. Math. 21, No. 1, Paper No. 25, 16 p. (2024)
Let $X$ be a Stein manifold of complex dimension $n>1$ endowed with a Riemannian metric $\mathfrak{g}$. We show that for every integer $k$ with $\left[\frac{n}{2}\right] \le k \le n-1$ there is a nonsingular holomorphic foliation of dimension $k$ on
Externí odkaz:
http://arxiv.org/abs/2305.06030
Autor:
Alarcon, Antonio, Forstneric, Franc
We introduce and study a new class of complex manifolds, Oka-1 manifolds, characterized by the property that holomorphic maps from any open Riemann surface to the manifold satisfy the Runge approximation and the Weierstrass interpolation conditions.
Externí odkaz:
http://arxiv.org/abs/2303.15855
Autor:
Alarcon, Antonio, Forstneric, Franc
Publikováno v:
Ann. Mat. Pura Appl. (4), 203:1673-1701, 2024
This paper brings several contributions to the classical Forster-Bell-Narasimhan conjecture and the Yang problem concerning the existence of proper and almost proper (hence complete) injective holomorphic immersions of open Riemann surfaces in the af
Externí odkaz:
http://arxiv.org/abs/2301.10304
Autor:
Alarcon, Antonio
We survey the history as well as recent progress in the Yang problem concerning the existence of complete bounded complex submanifolds of the complex Euclidean spaces. We also point out some open questions on the topic.
Externí odkaz:
http://arxiv.org/abs/2212.08521
Autor:
Alarcon, Antonio, Lopez, Francisco J.
We prove that every open Riemann surface admits a proper embedding into $\mathbb{R}^4$ by harmonic functions. This reduces by one the previously known embedding dimension in this framework, dating back to a theorem by Greene and Wu from 1975.
Externí odkaz:
http://arxiv.org/abs/2206.03566
Autor:
Alarcon, Antonio, Larusson, Finnur
The Gauss map of a conformal minimal immersion of an open Riemann surface $M$ into $\mathbb R^3$ is a meromorphic function on $M$. In this paper, we prove that the Gauss map assignment, taking a full conformal minimal immersion $M\to\mathbb R^3$ to i
Externí odkaz:
http://arxiv.org/abs/2205.10790