Monge Cone - Examples

Examples

Eikonal equation

The simplest fully nonlinear equation is the eikonal equation. This has the form

so that the function F is given by

The dual cone consists of 1-forms adx+bdy+cdz satisfying

Taken projectively, this defines a circle. The dual curve is also a circle, and so the Monge cone at each point is a proper cone.

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