https://neckpinch.com/authors/martin-reiris/New arXiv papers by Martin Reiris, from Neckpinch Tue, 03 Nov 2026 08:41:12 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 https://neckpinch.com/papers/2303.17385/arxiv:2303.17385Thu, 30 Mar 2023 00:00:00 GMTTheodora Bourni, Martin Reiris — We construct a slingshot, that is a compact, embedded solution to curve shortening flow that comes out of a non compact curve and exists for a finite time.Curve shorteningSingularitiesBoundaries & non-compact