Welcome to the Geometry Seminar of the Deparment of Geometry and Topology of the University of Granada. Here you can find information about the talks and events organized by the department.

# El teorema de Spruck y Xiao para solitones del flujo por la curvatura media

## Francisco Martín Serrano Universidad de Granada

Spruck y Xiao demostraron en 2018 que todo solitón por traslación del FCM en $\mathbb{R}^3$ que sea un grafo completo tiene que ser convexo $K \geq 0$. Nosotros daremos una demostración alternativa de ese teorema, basada en un trabajo conjunto con D. Hoffman y B. White.

Seminario 2ª planta, IEmath

# Holomorphicity of real Kaehler submanifolds

## Sergio Chion Pontificia Universidad Católica del Perú

I will discuss the subject of real Kaehler submanifolds, that is, isometric immersions $f\colon M^{2n}\to\mathbb{R}^{2n+p}$ of a Kaehler manifold $(M^{2n},J)$ of complex dimension $n\geq 2$ into Euclidean space with codimension $p$. In particular, I will present a recent result that shows that for codimension $2p\leq 2n-1$ generic rank conditions on the second fundamental form of $f$ imply that the submanifold has to be minimal. In fact, for codimension $p\leq 11$ we have a stronger conclusion, namely, that $f$ must be holomorphic with respect to some complex structure in the ambient space.

This is joint work with A. de Carvalho and M. Dajczer.

Despacho: Iemath

Despacho: IEMath

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