https://neckpinch.com/authors/ignacio-bustamante/New arXiv papers by Ignacio Bustamante, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2501.12949/arxiv:2501.12949Wed, 22 Jan 2025 00:00:00 GMTIgnacio Bustamante, Martin Reiris — In his groundbreaking work from 2002, Perelman introduced two fundamental monotonic quantities: the reduced volume and the entropy. While the reduced volume was motivated by the Bishop-Gromov volume comparison applied to a suitably constructed N-space, which becomes Ricci-flat as N→ ∞, Perelman did not provide a corresponding explanation for the origin of the entropy. In this article, we demonstrate that Perelman's entropy emerges as the limit of Colding's monotonic volume for harmonic functions on Ricci-flat manifolds, when appropriately applied to Perelman's N-space.Ricci-flat & Calabi–YauPerelman entropyReduced volume