 Area of a small geodesic polar ball under an upper curvature bound

ID: area-of-a-small-geodesic-polar-ball-under-an-upper-curvature-bound

K \leq C

with

C > 0

, scalar comparison gives

h (r, θ) \geq \frac{s i n ( C r )}{C}

before

π / C

. Consequently

Area B (p, ε) \geq \frac{2 π}{C} (1 - cos (C ε)) = π ε^{2} (1 + O (ε^{2})) .

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