Publications
2024
Simon, M.;
Preserving curvature lower bounds when Ricci flowing non-smooth initial data,
Surveys in Differential Geometry, Essays on Geometric Flows - Celebrating 40 Years of Ricci Flow, 27 (1) 147-187, (2024)
https://dx.doi.org/10.4310/SDG.241011021158
2023
Lamm, T., Simon, M.;
Ricci flow of W2,2-metrics in four dimensions,
Commentarii Mathematici Helvetici, Vol. 98, No. 2pp. 261–364(2023)
DOI 10.4171/CMH/553
2022
Simon, M., Topping, P. ;
Local control on the geometry in 3D Ricci flow,
Journal of Differential Geometry, 122(3) 467-518 November 2022.
https://doi.org/10.4310/jdg/1675712996
2021
Deruelle, A,; Schulze, F.; Simon, M. :
On the regularity of Ricci flows coming out of metric spaces,
JEMS, Vol. 24, No. 7pp. 2233–2277, (2021).
DOI 10.4171/JEMS/1138
Simon, M., Topping, P.,
Local mollication of Riemannian metrics using Ricci flow, and Ricci limit spaces,
Geometry Topology, Geom. Topol. 25(2), 913-948, (2021).
2020
Simon, M. :
Extending four dimensional Ricci flows with bounded scalar curvature,
Communications in analysis and geometry , Internat. Press, Bd. 28 ,7, S. 1683-1754, (2020)
Simon, M. :
Some integral curvature estimates for the Ricci flow in four dimensions ,
Communications in analysis and geometry , Internat. Press, Bd. 28. 3, S. 707-727, (2020)
2019
Bohm, C., Lafuente, R., , Simon, M. :
Optimal curvature estimates for homogeneous Ricci flows,
International Mathematics Research Notices, 14, pp. 4431-4468 (2019)
https://doi.org/10.1093/imrn/rnx256
2017
Simon, M.:
Ricci flow of Regions with Curvature Bounded Below in Dimension Three ,
J Geom Anal Volume 27, pp. 3051–3070 (2017).
doi:10.1007/s12220-017-9793-4
2014
Simon, Miles and Wheeler, Glen :
Some local estimates and a uniqueness result for the entire biharmonic heat equation ,
Advances in Calculus of Variations, (2014)
DOI: 10.1515/acv-2014-0027
2013
Simon, Miles :
Local smoothing results for the Ricci flow in dimensions two and three.
Geom. Topol. 17(4): 2263-2287 (2013)
DOI: 10.2140/gt.2013.17.2263
Schulze, Felix; Simon, Miles :
Expanding solitons with non-negative curvature operator coming out of cones
Math. Z. 275, 625–639 (2013)
https://doi.org/10.1007/s00209-013-1150-0
2012
Simon, Miles :
Ricci flow of non-collapsed 3-manifolds whose Ricci curvature is bounded from below.
J. reine angew. Math. 662, 59—94, (2012)
DOI: 10.1515/CRELLE.2011.088,
2011
Simon, M., Schulze, F., Schnurer,O.:
Stability of hyperbolic space under Ricci flow,
Communications in analysis and geometry ; 19 , 5. - S. 1023-1047, (2011)
2009
Simon, Miles :
Ricci flow of almost non-negatively curved three manifolds,
J. reine angew. Math. 630 (2009),
DOI 10.1515/CRELLE.2009.038
2008
Simon, Miles :
Local results for flows whose speed or height satisfies a bound of the form $\frac c t$.
International Mathematics Research Notices, Vol. 2008 : article ID rnn097, 14 pages, (2008)
Schnuerer, Oliver, Schulze, Felix, Simon, Miles :
Stability of Euclidean space under Ricci flow,
Communictions in Geom. and Ana., Volume 16, Number 1, 127–158, (2008).
2005
Simon, M.:
Ricci flow of almost non-negatively curved three manifolds,
Geometric evolution equations, 167 - 179, Contemp. Math., 367, Amer. Math. Soc., Providence, RI, (2005)
2004
Simon, Miles :
Deforming Lipschitz metrics into smooth metrics while keeping their curvature operator non-negative,
Geometric Evolution Equations, Hsinchu, Taiwan, July 15- August 14, 2002, edited by Ben Chow, Sun-Chin Chu, Chang-Shou Lin, Shu-Cheng Chang American Mathematical Society, (2004)
2002
Simon, Miles :
Deformation of C0 Riemannian metrics in the direction of their Ricci curvature,
Comm. Anal. Geom. 10, no. 5, 1033-1074, (2002).
Simon, Miles :
Some corrections to "C0 Riemannian metrics in the direction of their Ricci curvature":
PDF
2000
Simon, Miles:
A class of Riemannian manifolds which pinch when evolved by Ricci flow,
Manuscripta Mathematica, 101, no.1, (2000)