Minimal harmonic graphs and their Lorentzian cousins

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Motivated by the observation that the only surface which is locally a graph of a harmonic function and is also a minimal surface in E3 is either a plane or a helicoid, we provide similar characterizations of the elliptic, hyperbolic and parabolic helicoids in L3 as the nontrivial zero mean curvature surfaces which also satisfy the harmonic equation, the wave equation, and a degenerate equation which is derived from the harmonic equation or the wave equation. This elementary and analytic result shows that the change of the roles of dependent and independent variables may be useful in solving differential equations.

Original languageEnglish
Pages (from-to)666-670
Number of pages5
JournalJournal of Mathematical Analysis and Applications
Volume353
Issue number2
DOIs
Publication statusPublished - 2009 May 15

Keywords

  • Harmonic graph
  • Minimal surfaces
  • Wave graph
  • Zero mean curvature surfaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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