Heather Macbeth — Neckpinchhttps://neckpinch.com/authors/heather-macbeth/New arXiv papers by Heather Macbeth, from Neckpinch Tue, 03 Nov 2026 07:43:57 GMT Sharp L² estimates for the drift heat equation on shrinking Ricci solitonshttps://neckpinch.com/papers/2402.03304/arxiv:2402.03304Mon, 05 Feb 2024 00:00:00 GMTHeather Macbeth — We prove an L² estimate for the drift heat equation on a complete gradient shrinking Ricci soliton. This estimate has a time-dependent weight which is Gaussian in its spatial asymptotics. When transferred and scaled to an estimate for the heat equation along the Ricci flow of the soliton, this estimate is uniform up to the singular time.Ricci flowRicci solitons