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Isothermal Parameterization

A parameterization is isothermal if, for zeta=u+iv and

phi_k(zeta)=(partialx_k)/(partialu)-i(partialx_k)/(partialv),

the identity

phi_1^2(zeta)+phi_2^2(zeta)+phi_3^2(zeta)=0

holds.

See also

Minimal Surface, Temperature

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References

Osserman, R. "Isothermal Parameters." §4 in A Survey of Minimal Surfaces. New York: Dover, pp. 27-33, 1986.

Referenced on Wolfram|Alpha

Isothermal Parameterization

Cite this as:

Weisstein, Eric W. "Isothermal Parameterization." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IsothermalParameterization.html

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