Formal matched asymptotics for degenerate Ricci flow neckpinches
نویسندگان
چکیده
Gu and Zhu [16] have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on Sn+1 (n ≥ 2). In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit.
منابع مشابه
Degenerate Neckpinches in Ricci Flow
In earlier work [2], we derived formal matched asymptotic profiles for families of Ricci flow solutions developing Type-II degenerate neckpinches. In the present work, we prove that there do exist Ricci flow solutions that develop singularities modeled on each such profile. In particular, we show that for each positive integer k ≥ 3, there exist compact solutions in all dimensions m ≥ 3 that be...
متن کاملMinimally Invasive Surgery for Ricci Flow Singularities
In this paper, we construct smooth forward Ricci flow evolutions of singular initial metrics resulting from rotationally symmetric neckpinches on Sn+1, without performing an intervening surgery. In the restrictive context of rotational symmetry, this construction gives evidence in favor of Perelman’s hope for a “canonically defined Ricci flow through singularities”.
متن کاملRicci Flow Neckpinches without Rotational Symmetry
We study “warped Berger” solutions ( S1×S3, G(t) ) of Ricci flow: generalized warped products with the metric induced on each fiber {s}×SU(2) a left-invariant Berger metric. We prove that this structure is preserved by the flow, that these solutions develop finite-time neckpinch singularities, and that they asymptotically approach round product metrics in space-time neighborhoods of their singu...
متن کاملFormal Asymptotics of Bubbling in the Harmonic Map Heat Flow
The harmonic map heat flow is a model for nematic liquid crystals and also has origins in geometry. We present an analysis of the asymptotic behaviour of singularities arising in this flow for a special class of solutions which generalises a known (radially symmetric) reduction. Specifically, the rate at which blowup occurs is investigated in settings with certain symmetries using the method of...
متن کاملNeckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow
We study noncompact surfaces evolving by mean curvature flow (mcf). For an open set of initial data that are C3-close to round, but without assuming rotational symmetry or positive mean curvature, we show that mcf solutions become singular in finite time by forming neckpinches, and we obtain detailed asymptotics of that singularity formation. Our results show in a precise way that mcf solutions...
متن کامل