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This subtopic studies Riemann surfaces, connecting complex analysis with global surface geometry and the analytic continuation of multivalued functions.
30F10 studies compact riemann surfaces and uniformization in Riemann surfaces. It studies one-dimensional complex manifolds and the function theory that lives naturally on them.
Used to unify local analytic data with global topology in complex analysis.
30F15 studies harmonic functions on riemann surfaces in Riemann surfaces. It studies one-dimensional complex manifolds and the function theory that lives naturally on them.
Used to unify local analytic data with global topology in complex analysis.
30F20 studies classification theory of riemann surfaces in Riemann surfaces. It studies one-dimensional complex manifolds and the function theory that lives naturally on them.
Used to unify local analytic data with global topology in complex analysis.
30F25 studies ideal boundary theory for riemann surfaces in Riemann surfaces. It studies one-dimensional complex manifolds and the function theory that lives naturally on them.
Used to unify local analytic data with global topology in complex analysis.
30F30 studies differentials on riemann surfaces in Riemann surfaces. It studies one-dimensional complex manifolds and the function theory that lives naturally on them.
Used to unify local analytic data with global topology in complex analysis.
30F35 studies fuchsian groups and automorphic functions in Riemann surfaces. It studies one-dimensional complex manifolds and the function theory that lives naturally on them.
Used to unify local analytic data with global topology in complex analysis.
30F40 studies kleinian groups and hyperbolic $3$-manifolds in Riemann surfaces. It studies one-dimensional complex manifolds and the function theory that lives naturally on them.
Used to unify local analytic data with global topology in complex analysis.
30F45 studies conformal metrics (hyperbolic, poincarã©, distance functions) in Riemann surfaces. It studies one-dimensional complex manifolds and the function theory that lives naturally on them.
Used to unify local analytic data with global topology in complex analysis.
30F50 studies klein surfaces in Riemann surfaces. It studies one-dimensional complex manifolds and the function theory that lives naturally on them.
Used to unify local analytic data with global topology in complex analysis.
30F60 studies teichmã¼ller theory for riemann surfaces in Riemann surfaces. It studies one-dimensional complex manifolds and the function theory that lives naturally on them.
Used to unify local analytic data with global topology in complex analysis.