33 citations · 138 across the 31 of their papers we have counts for
39 papers
Smoothing polyhedral spaces via Ricci flow
Richard H. Bamler, Esther Cabezas-Rivas
We prove Petrunin's smoothing conjecture in all dimensions: every compact Euclidean polyhedral space without boundary and with nonnegative Alexandrov curvature is a Gromov-Hausdorf…
A non-Kähler expanding Ricci soliton with a Kähler tangent cone at infinity
Richard H. Bamler, Eric Chen, Ronan J. Conlon
We construct an example of an asymptotically conical (AC) non-Kähler expanding gradient Ricci soliton that has a Kähler tangent cone at infinity. This yields an example of a Kähler…
The PDE-ODI principle and cylindrical mean curvature flows
Richard H. Bamler, Yi Lai
We introduce a new approach for analyzing ancient solutions and singularities of mean curvature flow that are locally modeled on a cylinder. Its key ingredient is a general mechani…
Classification of ancient cylindrical mean curvature flows and the Mean Convex Neighborhood Conjecture
Richard H. Bamler, Yi Lai
We resolve the Mean Convex Neighborhood Conjecture for mean curvature flows in all dimensions and for all types of cylindrical singularities. Specifically, we show that if the tang…
On the Multiplicity One Conjecture for Mean Curvature Flows of surfaces
Richard H Bamler, Bruce Kleiner
We prove the Multiplicity One Conjecture for mean curvature flows of surfaces in . Specifically, we show that any blow-up limit of such mean curvature flows has multi…
Degree theory for 4-dimensional asymptotically conical gradient expanding solitons
Richard H. Bamler, Eric Chen
We develop a new degree theory for 4-dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymp…
A new complete two-dimensional shrinking gradient Kähler-Ricci soliton
Richard H. Bamler, Charles Cifarelli, Ronan J. Conlon +1
We prove the existence of a unique complete shrinking gradient Kähler-Ricci soliton with bounded scalar curvature on the blowup of at one point. Th…
Decomposing 4-manifolds with positive scalar curvature
Richard H. Bamler, Chao Li, Christos Mantoulidis
We show that every closed, oriented, topologically PSC 4-manifold can be obtained via 0 and 1-surgeries from a topologically PSC 4-orbifold with vanishing first Betti number and se…
An optimal volume growth estimate for noncollapsed steady gradient Ricci solitons
Richard H. Bamler, Pak-Yeung Chan, Zilu Ma +1
In this paper, we prove a volume growth estimate for steady gradient Ricci solitons with bounded Nash entropy. We show that such a steady gradient Ricci soliton has volume growth r…
On the fundamental group of non-collapsed ancient Ricci flows
Richard H. Bamler
We show that any manifold admitting a non-collapsed, ancient Ricci flow must have finite fundamental group. This generalizes what was known for -solutions in dimensions 2, 3. We…
Diffeomorphism groups of prime 3-manifolds
Richard H. Bamler, Bruce Kleiner
Let be a compact orientable non-Haken 3-manifold modeled on the Thurston geometry . We show that the diffeomorphism group deformation retracts to t…
Recent developments in Ricci flows
Richard H Bamler
This is a survey on recent developments in Ricci flows.
Four-Dimensional Steady Gradient Ricci Solitons with -Cylindrical Tangent Flows at Infinity
Richard Bamler, Bennett Chow, Yuxing Deng +2
In this paper we consider -dimensional steady soliton singularity models, i.e., complete steady gradient Ricci solitons that arise as the rescaled limit of a finite time singula…
Structure theory of non-collapsed limits of Ricci flows
Richard H Bamler
In this paper we characterize non-collapsed limits of Ricci flows. We show that such limits are smooth away from a set of codimension in the parabolic sense and that the t…
Compactness theory of the space of Super Ricci flows
Richard H Bamler
We develop a compactness theory for super Ricci flows, which lays the foundations for the partial regularity theory in [Bam20b]. Our results imply that any sequence of super Ricci…
Entropy and heat kernel bounds on a Ricci flow background
Richard H Bamler
In this paper we establish new geometric and analytic bounds for Ricci flows, which will form the basis of a compactness, partial regularity and structure theory for Ricci flows in…
Ricci flow and contractibility of spaces of metrics
Richard H. Bamler, Bruce Kleiner
We show that the space of metrics of positive scalar curvature on any 3-manifold is either empty or contractible. Second, we show that the diffeomorphism group of every 3-dimension…
On the rotational symmetry of 3-dimensional -solutions
Richard H. Bamler, Bruce Kleiner
In a recent paper, Brendle showed the uniqueness of the Bryant soliton among 3-dimensional -solutions. In this paper, we present an alternative proof for this fact and show that…
Ricci flow and diffeomorphism groups of 3-manifolds
Richard H. Bamler, Bruce Kleiner
We complete the proof of the Generalized Smale Conjecture, apart from the case of , and give a new proof of Gabai's theorem for hyperbolic 3-manifolds. We use an approach bas…
Uniqueness and stability of Ricci flow through singularities
Richard H. Bamler, Bruce Kleiner
We verify a conjecture of Perelman, which states that there exists a canonical Ricci flow through singularities starting from an arbitrary compact Riemannian 3-manifold. Our main r…
The Ricci flow under almost non-negative curvature conditions
Richard H. Bamler, Esther Cabezas-Rivas, Burkhard Wilking
We generalize most of the known Ricci flow invariant non-negative curvature conditions to less restrictive negative bounds that remain sufficiently controlled for a short time. As…
Structure theory of singular spaces
Richard H. Bamler
In this paper we generalize the theory of Cheeger, Colding and Naber to certain singular spaces that arise as limits of sequences of Riemannian manifolds. This theory will have app…
Convergence of Ricci flows with bounded scalar curvature
Richard H. Bamler
In this paper we prove convergence and compactness results for Ricci flows with bounded scalar curvature and entropy. More specifically, we show that Ricci flows with bounded scala…
Compactness properties of Ricci flows with bounded scalar curvature
Richard H. Bamler
In this paper we prove a compactness result for Ricci flows with bounded scalar curvature and entropy. It states that given any sequence of such Ricci flows, we can pass to a subse…