Research interests

• Ricci flow, singular metric spaces, mean curvature flow, singularities of Ricci and mean-curvature flow, geometric flows, geometric flows with surgery, parabolic and elliptic differential equations, global geometry, compactness theorems in geometry.

Honours Year (Undergraduate) :

• Mean curvature flow of rotationally symmetric hypersurfaces( 1990) Mean curvature flow of rotationally symmetric hypersurfaces( 1990)

PhD Thesis:

• A class of manifolds that pinch when evolved by Ricci flow, (1998)

Habilitation Thesis:

• Selected chapters from my Habilitation thesis   pdf "Ricci flow of almost non-negatively curved three manifolds",Universität Freiburg, Deutschland, Nov. 2006

Dr. Florian Litzinger

Priyamvada Vishwamitra

Seminar with Hannover: Differential Geometry and Analysis

Seminar: Geometric Analysis

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)