Minimal harmonic graphs and their Lorentzian cousins

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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
Issue number2
Publication statusPublished - 2009 May 15

Bibliographical note

Funding Information:
We thank J. Inoguchi for pointing out Kobayashi’s result. The first and the last authors were supported in part by Korea University research grants.


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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


Dive into the research topics of 'Minimal harmonic graphs and their Lorentzian cousins'. Together they form a unique fingerprint.

Cite this