We attempt to provide a mesoscopic treatment of the origin of black hole entropy in (3+1)-dimensional spacetimes. We treat the case of horizons having space-like sections Σ which are topological spheres, following Hawking's and the Topological Censorship theorems. We use the injectivity radius of the induced metric on Σ to encode the linear dimensions of the elementary cells giving rise to such entropy. We use the topological entropy of Σ as the fundamental quantity expressing the complexity of

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... Σ on which its entropy depends. We point out the significance, in this context, of the Berger and Croke isoembolic inequalities.