Evaluating integral on surfaces

  1. Hello everyone! Could someone tell me how to evaluate the integral
    [tex]
    \int_{B_{\delta}(p_0)}{\frac{1}{(1 + d^2(p_0, p))^2}\mathrm{d}v_g(p)}
    [/tex]
    where [itex]B_{\delta}(p_0) \subset M[/itex] and [itex](M, g)[/itex] is a generic compact surface and [itex]\delta > 0[/itex] can be made small as one wishes (as usual, [itex]d[/itex] is the intrinsic metric)? Thanks you in advance

    P.S. I strongly suspect that the value should be [itex]\pi[/itex], but I'm a newbie in integration-on-manifold without any idea about how to proceed.
     
  2. jcsd
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