Asian Journal of Mathematics

Volume 19 (2015)

Number 4

Simplicial energy and simplicial harmonic maps

Pages: 593 – 636



Joel Hass (Department of Mathematics, University of California at Davis)

Peter Scott (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)


We introduce a combinatorial energy for maps of triangulated surfaces with simplicial metrics and analyze the existence and uniqueness properties of the corresponding harmonic maps. We show that some important applications of smooth harmonic maps can be obtained in this setting.


harmonic map, energy, area, minimal surface

2010 Mathematics Subject Classification


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Published 4 November 2015