Some Geometric Aspects of the Hessian One Equation

  • Antonio Martínez
  • Francisco Milán
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)


The Hessian one equation and its complex resolution provides an important tool in the study of improper affine spheres in \(\mathbb{R}^{3}\) with some kind of singularities. The singular set can be characterized and, in most of the cases, it determines the surface. Here, we show how to obtain improper affine spheres with a prescribed singular set and construct some global examples with the desired singularities. We also classify improper affine spheres admitting a planar singular set.


Conformal Structure Entire Solution Complex Resolution Singular Curve Isolate Singularity 
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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.University of GranadaGranadaSpain

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