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11	A New Approach to Lie Symmetry Groups of Minimal Surfaces Berry, Robert D. 18 June 2004 (has links) (PDF) The Lie symmetry groups of minimal surfaces by way of planar harmonic functions are determined. It is shown that a symmetry group acting on the minimal surfaces is isomorphic with H × H^2 — the analytic functions and the harmonic functions. A subgroup of this gives a generalization of the associated family which is examined. minimal surfaces Lie groups harmonic associated family symmetry geometric function theory Mathematics
12	Module structure of a Hilbert space Leon, Ralph Daniel 01 January 2003 (has links) This paper demonstrates the properties of a Hilbert structure. In order to have a Hilbert structure it is necessary to satisfy certain properties or axioms. The main body of the paper is centered on six questions that develop these ideas. Hilbert space Invariant subspaces Kernel functions Functions of complex variables Geometric function theory
13	The Lie Symmetries of a Few Classes of Harmonic Functions Petersen, Willis L. 23 May 2005 (has links) (PDF) In a differential geometry setting, we can analyze the solutions to systems of differential equations in such a way as to allow us to derive entire classes of solutions from any given solution. This process involves calculating the Lie symmetries of a system of equations and looking at the resulting transformations. In this paper we will give a general background of the theory necessary to develop the ideas of working in the jet space of a given system of equations, applying this theory to harmonic functions in the complex plane. We will consider harmonic functions in general, harmonic functions with constant Jacobian, harmonic functions with fixed convexity and a few other subclasses of harmonic functions. Lie symmetries harmonic functions area preserving Lie group geometric function theory schlicht functions differential geometry manifolds Lie algebra Mathematics

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