Univerza v Ljubljani

Seminario de Geometría

Ponente: Franc Forstneric (Univerza v Ljubljani, Eslovenia)

Día y hora: 9 de febrero de 2018, de 11:30 a 12:30

Lugar: Seminario 1, IEMath-GR



Título: A properly embedded holomorphic disc in the ball with finite area and dense boundary curve

Resumen: I will describe the construction of a properly embedded holomorphic disc in the unit ball of $\mathbb{C}^2$ having the following surprising combination of properties:


On the one hand, the disc has finite area, and hence is the zero set of a bounded holomorphic function on the ball.


On the other hand, its real analytic boundary curve is everywhere dense in the sphere.

Title: The parametric h-principle for minimal surfaces in $R^n$
and null curves in $C^n$

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Speaker: Franc Forstneric (Univerza v Ljubljani)

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Abstract: Let M be an open Riemann surface. It was proved by Alarcón and Forstneric that every conformal minimal immersion M→$R^3$ is isotopic to the real part of a holomorphic null curve M→$C^3$. We prove the following substantially stronger result in this direction: for any n≥3, the inclusion of the space of real parts of non flat null holomorphic immersions M→$C^n$ into the space of non flat conformal minimal immersions M→$R^n$ satisfies the parametric h-principle with approximation; in particular, it is a weak homotopy equivalence. Analogous results hold for several other related maps. For an open Riemann surface M of finite topological type, we obtain optimal results by showing that the above inclusion and several related maps are inclusions of strong deformation retracts; in particular, they are homotopy equivalences. (Joint work with Finnur Lárusson.)

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18 March 2016, 11:30, 1st floor Seminar room, IEMath-GR

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More information about the Geometry Seminar in http://wdb.ugr.es/~geometry/seminar/es