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3-manifolds abstract algorithm analytic asymptotic automorphism Banach algebra Banach space boundary bounded C*-algebra coefficients cohomology compact complex Computer conjecture construct convergence convex curvature curve December 12 defined denote Department of Mathematics differential equations dimension dimensional discuss domain eigenvalues elements elliptic equivalent existence extension finite functions geometry graph holomorphic homotopy hyperbolic ideal inequality infinite integral invariant inverse irreducible isomorphic lattice Lie algebra Lie group linear manifold Math matrix maximal mean curvature method metric minimal modules moduli space nonlinear obtained October 11 operators optimal paper parameter partial differential equations polynomials Preliminary report problem properties prove quantum quantum groups Received August Received December 12 Received January Received July Received November Received October 11 Received September representation Riemann surface Riemannian manifold ring semigroup sequence singular solutions spectral Sponsored structure subgroup subset surface theorem theory topology University variables vector