AbstractIt is well-known that any plane polygon can be decomposed along its diagonals into flat triangles. The analog does not hold for spherical polygons. We prove that any compact surface with constant positive curvature and conical singularities can be decomposed into irreducible components of standard shape, glued along geodesic arcs connecting conical singularities. The irreducible compone...
AbstractI will first give an overview of some aspects of integrable quad-graph systems . This includes the notion of multi-dimensional consistency, classification results of quad-equations, connections to complex analysis. Then, I will show how to implement initial-boundary value problems for quad-graph systems. It relies on the notion of boundary consistency that defines integrable boundary co...
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