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Wolf, Michael Stockton, George F. 2009-06-03T23:58:51Z 2009-06-03T23:58:51Z 1991 Stockton, George F.. "Harmonic maps of trivalent trees." (1991) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/13512">https://hdl.handle.net/1911/13512</a>. https://hdl.handle.net/1911/13512 Thesis Math. 1991 Stockton This thesis is a study of harmonic maps of trivalent trees into Euclidean space. The existence of such maps is established, and uniqueness is shown to hold up to a certain isotopy condition. Moreover, within its particular isotopy class, each harmonic map is shown to be a local minimum for the energy functional. A harmonic map of a trivalent tree is determined by its associated nodes. Collectively, these nodes are a function of the lengths of the parameter spaces of the paths which comprise the map. It is shown that this node function can be continuously extended to certain parts of the boundary of its domain; these parts of the boundary are closely related to the geometry of the trivalent tree which serves as the domain of the given harmonic map. 44 p. application/pdf eng Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. Mathematics Harmonic maps of trivalent trees Thesis Text Mathematics Natural Sciences Rice University Masters Master of Arts open.access