 Area of a geodesic polar ball with nonpositive curvature

ID: area-of-a-geodesic-polar-ball-with-nonpositive-curvature

K \leq 0

, then

h_{rr} = - K h \geq 0

, so

h \geq r

. Every geodesic polar ball of radius

ε

therefore satisfies

Area B (p, ε) \geq π ε^{2} .

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