Max Planck Institute for Mathematics in the Sciences

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19972026

most citedOn the Number of Linear Regions of Deep Neural Networks

832 citations

Showing 2019 · math.DGShow all

4 papers · 2 filters

math.DG2019★ 8 cited

Short-time existence of the $α$ -Dirac-harmonic map flow and applications

Jürgen Jost, Jingyong Zhu

In this paper, we discuss the general existence theory of Dirac-harmonic maps from closed surfaces via the heat flow for $α$ -Dirac-harmonic maps and blow-up analysis. More precisel…

math.DG2019

Realizing the Teichmüller space as a symplectic quotient

Tobias Diez, Tudor S. Ratiu

Given a closed surface endowed with a volume form, we equip the space of compatible Riemannian structures with the structure of an infinite-dimensional symplectic manifold. We show…

math.DG2019★ 2 cited

Central extensions of Lie groups preserving a differential form

Tobias Diez, Bas Janssens, Karl-Hermann Neeb +1

Let $M$ be a manifold with a closed, integral $(k + 1)$ -form $ω$ , and let $G$ be a Fréchet-Lie group acting on $(M, ω)$ . As a generalization of the Kostant-Souriau extension for sympl…

math.DG2019★ 5 cited

$α$ -Dirac-harmonic maps from closed surfaces

Jürgen Jost, Jingyong Zhu

$α$ -Dirac-harmonic maps are variations of Dirac-harmonic maps, analogous to $α$ -harmonic maps that were introduced by Sacks-Uhlenbeck to attack the existence problem for harmonic m…

Short-time existence of the α-Dirac-harmonic map flow and applications

Realizing the Teichmüller space as a symplectic quotient

Central extensions of Lie groups preserving a differential form

α-Dirac-harmonic maps from closed surfaces

Short-time existence of the $α$ -Dirac-harmonic map flow and applications

$α$ -Dirac-harmonic maps from closed surfaces