We offer a new approach to proving the Chen-Donaldson-Sun theorem which we demonstrate with a series of examples. We discuss the existence of a construction of a special metric on stable vector bundles over the surfaces formed by a families of curves and its relation to the one-dimensional cycles in the moduli space of stable bundles on curves.
On the kernel of the Laplace operator on two-dimensional polyhedra E. N. Lukzen & A. I. Shafarevich
We prove that space of harmonic functions on polyhedra is isomorphic to the intersection of the plane defining the Laplacian with a chosen Lagrangian plane depending only on the polyhedron, and give explicit examples of harmonic functions on spherical polyhedra in terms of the natural complex structure on these objects.