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Minimal harmonic graphs and their Lorentzian cousins
- Issue Date
- 15-5월-2009
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Harmonic graph; Wave graph; Minimal surfaces; Zero mean curvature surfaces
- Citation
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.353, no.2, pp.666 - 670
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- Volume
- 353
- Number
- 2
- Start Page
- 666
- End Page
- 670
- ISSN
- 0022-247X
- 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 E-3 is either a plane or a helicoid, we provide similar characterizations of the elliptic, hyperbolic and parabolic helicoids in L-3 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. (C) 2009 Elsevier Inc. All rights reserved.
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