22 citations · 30 across the 6 of their papers we have counts for
9 papers
Delaunay decompositions minimizing energy of weighted toroidal graphs
Wai Yeung Lam
Given a weighted toroidal graph, each realization to a Euclidean torus is associated with the Dirichlet energy. By minimizing the energy over all possible Euclidean structures and…
CMC-1 surfaces via osculating Möbius transformations between circle patterns
Wai Yeung Lam
Given two circle patterns of the same combinatorics in the plane, the Möbius transformations mapping circumdisks of one to the other induces a -valued function o…
Quadratic differentials and circle patterns on complex projective tori
Wai Yeung Lam
Given a triangulation of a closed surface, we consider a cross ratio system that assigns a complex number to every edge satisfying certain polynomial equations per vertex. Every cr…
Dimers and Circle patterns
Richard Kenyon, Wai Yeung Lam, Sanjay Ramassamy +1
We establish a correspondence between the dimer model on a bipartite graph and a circle pattern with the combinatorics of that graph, which holds for graphs that are either planar…
Holomorphic quadratic differentials on graphs and the chromatic polynomial
Richard Kenyon, Wai Yeung Lam
We study "holomorphic quadratic differentials" on graphs. We relate them to the reactive power in an LC circuit, and also to the chromatic polynomial of a graph. Specifically, we s…
Infinitesimal conformal deformations of triangulated surfaces in space
Wai Yeung Lam, Ulrich Pinkall
We study infinitesimal conformal deformations of a triangulated surface in Euclidean space and investigate the change in its extrinsic geometry. A deformation of vertices is confor…
Discrete minimal surfaces: critical points of the area functional from integrable systems
Wai Yeung Lam
We obtain a unified theory of discrete minimal surfaces based on discrete holomorphic quadratic differentials via a Weierstrass representation. Our discrete holomorphic quadratic d…
Holomorphic vector fields and quadratic differentials on planar triangular meshes
Wai Yeung Lam, Ulrich Pinkall
Given a triangulated region in the complex plane, a discrete vector field assigns a vector to every vertex. We call such a vector field holomorphic if it de…
Isothermic triangulated surfaces
Wai Yeung Lam, Ulrich Pinkall
We found a class of triangulated surfaces in Euclidean space which have similar properties as isothermic surfaces in Differential Geometry. We call a surface isothermic if it admit…