https://neckpinch.com/authors/michael-b-law/New arXiv papers by Michael B. Law, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2505.20576/arxiv:2505.20576Mon, 26 May 2025 00:00:00 GMTMichael B. Law — We establish a symmetry principle for asymptotically cylindrical steady gradient Ricci solitons (GRSs) and asymptotically conical expanding GRSs with homogeneous links. Using this, we show that the Bryant steady soliton is the unique asymptotically cylindrical steady GRS that has a round spherical link and satisfies a particular quantitative rigidity condition. A similar characterization is proved for Bryant's expanding solitons. Finally, we establish a global symmetry result for GRSs which exhibit the aforementioned asymptotics with quotient-Berger sphere asymptotic links.Ricci solitonsHomogeneous spacesStability & uniquenessBoundaries & non-compact https://neckpinch.com/papers/2501.05119/arxiv:2501.05119Thu, 09 Jan 2025 00:00:00 GMTMichael B. Law — We construct and classify all polynomial growth solutions to certain drift-harmonic equations on complete manifolds with paraboloidal asymptotics. These encompass the natural drift-harmonic equations on certain steady gradient Ricci solitons. Specifically, we show that all drift-harmonic functions with polynomial growth asymptotically separate variables, and compute the dimensions of spaces of drift-harmonic functions with a given polynomial growth rate. The proof uses an inductive argument that alternates between constructing and asymptotically controlling drift-harmonic functions.Ricci solitonsBoundaries & non-compact