Gradient variational problems in ℝ²

2020/06/01 by Richard Kenyon, Kenyon, Richard, István Prause +1 · 2 citations
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2006.01219

openalex publication_date 2020/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a new integrability principle for gradient variational problems in ℝ², showing that solutions are explicitly parameterized by κ-harmonic functions, that is, functions which are harmonic for the laplacian with varying conductivity κ, where κ is the square root of the Hessian determinant of the surface tension.

Citations

• Dimer model, bead model and standard Young tableaux: finite cases and limit shapes
• Dimer Models and Conformal Structures

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• Kenyon's identities for the height function and compactified free field in the dimer model
• A quantum N-dimer model

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