On Functions with a Conjugate
Copyright policy )On Functions with a Conjugate
Harmonic functions of two variables are exactly those that admit a conjugate, namely a function whose gradient has the same length and is everywhere orthogonal to the gradient of the original function. We show that there are also partial differential equations controlling the functions of three variables that admit a conjugate.
- University of Adelaide Australia
- Australian National University Australia
Mathematics - Differential Geometry, conformal differential invariants, Differential geometric aspects of harmonic maps, 53A30, partial differential inequalities, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, 3-harmonic functions, partial differential inequality, conformal invariant, Differential Geometry (math.DG), partial differential equation, conformal Killing field, FOS: Mathematics, conjugate function, conjugate functions, 3-harmonic function
Mathematics - Differential Geometry, conformal differential invariants, Differential geometric aspects of harmonic maps, 53A30, partial differential inequalities, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, 3-harmonic functions, partial differential inequality, conformal invariant, Differential Geometry (math.DG), partial differential equation, conformal Killing field, FOS: Mathematics, conjugate function, conjugate functions, 3-harmonic function
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