28 citations · 107 across the 16 of their papers we have counts for
16 papers
A Local Singularity Analysis for the Ricci Flow and its Applications to Ricci Flows with Bounded Scalar Curvature -- Part II
Reto Buzano, Gianmichele Di Matteo
We continue our local singularity analysis for Ricci flow initiated in ArXiv:2006.16227. Building on that framework, we study Type I singular points in general Ricci flows, without…
Geometric Structure of Ends of Ricci Shrinkers
Alessandro Bertellotti, Reto Buzano
We study blow-up sequences of Ricci shrinkers without global curvature assumptions based at points at which the scalar curvature satisfies a Type I bound, proving that their $\…
Ends of (singular) Ricci shrinkers
Alessandro Bertellotti, Reto Buzano
We estimate the number of ends of smooth and singular Ricci shrinkers focussing first on general ends and later on asymptotically conical ones. In particular, we obtain a variety o…
Mean Curvature Flow and Heegaard Surfaces in Lens Spaces
Reto Buzano, Sylvain Maillot
We prove that the moduli space of mean convex two-spheres embedded in complete, orientable 3-dimensional Riemannian manifolds with nonnegative Ricci curvature is path-connected. Th…
Bubble-Tree Convergence and Local Diffeomorphism Finiteness for Gradient Ricci Shrinkers
Reto Buzano, Louis Yudowitz
We prove bubble-tree convergence of sequences of gradient Ricci shrinkers with uniformly bounded entropy and uniform local energy bounds, refining the compactness theory of Haslhof…
Noncompact self-shrinkers for mean curvature flow with arbitrary genus
Reto Buzano, Huy The Nguyen, Mario B. Schulz
In his lecture notes on mean curvature flow, Ilmanen conjectured the existence of noncompact self-shrinkers with arbitrary genus. Here, we employ min-max techniques to give a rigor…
Gaussian upper bounds for the heat kernel on evolving manifolds
Reto Buzano, Louis Yudowitz
In this article, we prove a general and rather flexible upper bound for the heat kernel of a weighted heat operator on a closed manifold evolving by an intrinsic geometric flow. Th…
A Local Singularity Analysis for the Ricci Flow and its Applications to Ricci Flows with Bounded Scalar Curvature
Reto Buzano, Gianmichele Di Matteo
We develop a refined singularity analysis for the Ricci flow by investigating curvature blow-up rates locally. We first introduce general definitions of Type I and Type II singular…
Bubbling analysis and geometric convergence results for free boundary minimal surfaces
Lucas Ambrozio, Reto Buzano, Alessandro Carlotto +1
We investigate the limit behaviour of sequences of free boundary minimal hypersurfaces with bounded index and volume, by presenting a detailed blow-up analysis near the points wher…
Geometric convergence results for closed minimal surfaces via bubbling analysis
Lucas Ambrozio, Reto Buzano, Alessandro Carlotto +1
We present some geometric applications, of global character, of the bubbling analysis developed by Buzano and Sharp for closed minimal surfaces, obtaining smooth multiplicity one c…
The higher-dimensional Chern-Gauss-Bonnet formula for singular conformally flat manifolds
Reto Buzano, Huy The Nguyen
In a previous article, we generalised the classical four-dimensional Chern-Gauss-Bonnet formula to a class of manifolds with finitely many conformally flat ends and singular points…
The moduli space of two-convex embedded tori
Reto Buzano, Robert Haslhofer, Or Hershkovits
In this short article we investigate the topology of the moduli space of two-convex embedded tori . We prove that for this mod…
The moduli space of two-convex embedded spheres
Reto Buzano, Robert Haslhofer, Or Hershkovits
We prove that the moduli space of 2-convex embedded n-spheres in R^{n+1} is path-connected for every n. Our proof uses mean curvature flow with surgery and can be seen as an extrin…
Qualitative and quantitative estimates for minimal hypersurfaces with bounded index and area
Reto Buzano, Ben Sharp
We prove qualitative estimates on the total curvature of closed minimal hypersurfaces in closed Riemannian manifolds in terms of their index and area, restricting to the case where…
Smooth long-time existence of Harmonic Ricci Flow on surfaces
Reto Buzano, Melanie Rupflin
We prove that at a finite singular time for the Harmonic Ricci Flow on a surface of positive genus both the energy density of the map component and the curvature of the domain mani…
The Chern-Gauss-Bonnet formula for singular non-compact four-dimensional manifolds
Reto Buzano, Huy The Nguyen
We generalise the classical Chern-Gauss-Bonnet formula to a class of 4-dimensional manifolds with finitely many conformally flat ends and singular points. This extends results of C…