Evaluating integral on surfaces

by Goklayeh
Tags: evaluating, integral, surfaces
Goklayeh is offline
Mar25-12, 04:12 PM
P: 17
Hello everyone! Could someone tell me how to evaluate the integral
\int_{B_{\delta}(p_0)}{\frac{1}{(1 + d^2(p_0, p))^2}\mathrm{d}v_g(p)}
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.
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