• Corpus ID: 117391385

Surfaces with radially symmetric prescribed Gauss curvature

  title={Surfaces with radially symmetric prescribed Gauss curvature},
  author={Sagun Chanillo and Michael K.-H. Kiessling},
  journal={arXiv: Analysis of PDEs},
We study conformally flat surfaces with prescribed Gaussian curvature, described by solutions $u$ of the PDE: $\Delta u(x)+K(x)\exp(2u(x))=0$, with $K(x)$ the Gauss curvature function at $x\in\RR^2$. We assume that the integral curvature is finite. For radially symmetric $K$ we introduce the notion of a least integrally curved surface, and also the notion of when such a surface is critical. With respect to these notions we analyze the radial symmetry of $u$ for the whole spectrum of possible… 

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