https://neckpinch.com/authors/boris-botvinnik/New arXiv papers by Boris Botvinnik, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1901.11169/arxiv:1901.11169Thu, 31 Jan 2019 00:00:00 GMTBoris Botvinnik, Peng Lu — Let W be a manifold with boundary M given together with a conformal class bar C which restricts to a conformal class C on M. Then the relative Yamabe constant Y_(bar C)(W,M;C) is well-defined. We study the short-time behavior of the relative Yamabe constant Y_([bar gₜ])(W,M;C) under the Ricci flow bar gₜ on W with boundary conditions that mean curvature H_(bar gₜ)≡ 0 and gₜ|_M∈ C = [g₀]. In particular, we show that if the initial metric g₀ is a Yamabe metric, then, under some natural assumptions, d/dt|ₜ₌₀Y_([bar gₜ])(W,M;C)≥ 0 and is equal to zero if and only the metric g₀ is Einstein.Ricci flowBoundaries & non-compact