Singularities of improper affine maps and their Hessian equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:405

Article

Milan, Francisco

关键词: Improper affine spheres;    Unimodular Hessian equation;    Cuspidal edges;    Swallowtails;    Isolated singularities;   

DOI  :  10.1016/j.jmaa.2013.03.057

来源: Elsevier

【 摘 要 】

We study improper affine spheres with some admissible singularities, called improper affine maps, and associated to the unimodular Hessian equation. In particular, we characterize when a curve of R-3 is the singular curve of some improper affine map with prescribed cuspidal edges and swallowtails. Also, we consider improper affine maps with isolated singularities and show some similarities and differences between the Hessian +1 equation and the Hessian -1 equation. As a consequence, we construct global examples with the desired singularities. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free