Prof. Dr. Miles Simon
Forschungsinteressen
- 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)
Dissertation:
- A class of manifolds that pinch when evolved by Ricci flow, (1998)
Habilitation:
- Selected chapters from my Habilitation thesis pdf "Ricci flow of almost non-negatively curved three manifolds",Universität Freiburg, Deutschland, Nov. 2006
laufende Veranstaltungen
SoSe 2020 | Analysis II |
SoSe 2020 | Mathematik 2a für Ing. (Stg A) |
bisherige Veranstaltungen
2017
Simon, M.:
Ricci flow of Regions with Curvature Bounded Below in Dimension Three,
J Geom Anal (2017). doi:10.1007/s12220-017-9793-4
Ricci flow of Regions with Curvature Bounded Below in Dimension Three
2016
Simon, M., Topping, P. :
Local control on the geometry in 3D Ricci flow, Arxiv Preprint (2016), arXiv:1611.06137
Local control on the geometry in 3D Ricci flow
Boehm, C., Lafuente, R., Simon, M. :
Optimal curvature estimates for homogeneous Ricci flows, Arxiv Preprint (2016), arXiv:1604.02625
Optimal curvature estimates for homogeneous Ricci flows
2015
Simon, Miles :
Extending four dimensional Ricci flows with bounded scalar curvature, Arxiv Preprint (2015), arXiv:1504.02910
Extending four dimensional Ricci flows with bounded scalar curvature
Simon, Miles :
Some integral curvature estimates for the Ricci flow in four dimensions , Arxiv Preprint (2015), arXiv:1504.02623
Some integral curvature estimates for the Ricci flow in four dimensions
2014
Simon, Miles and Wheeler, Glen :
Some local estimates and a uniqueness result for the entire biharmonic heat equation , Advances in Calculus of Variations, DOI: 10.1515/acv-2014-0027, December 2014
Some local estimates and a uniqueness result for the entire biharmonic heat equation
2013
Simon, Miles :
Local smoothing results for the Ricci flow in dimensions two and three. accepted March 2013, by the journal "Geometry and topology"
Local smoothing results for the Ricci flow in dimensions two and three
Schulze, Felix; Simon, Miles :
Expanding solitons with non-negative curvature operator coming out of cones Mathematische Zeitschrift, DOI 10.1007/s00209-013-1150-0,Accepted: 5 February 2013
Expanding solitons with non-negative curvature operator coming out of cones
2012
Simon, Miles :
Ricci flow of non-collapsed 3-manifolds whose Ricci curvature is bounded from below. Journal fuer die reine und angewandte Mathematik (Crelle), DOI: 10.1515/CRELLE.2011.088, January 2012
Ricci flow of non-collapsed 3-manifolds whose Ricci curvature is bounded from below
2008
Simon, Miles :
Local results for flows whose speed or height satisfies a bound of the form $\frac c t$. International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn097, 14 pages, (2008)
Local results for flows whose speed or height satisfies a bound of the form $\frac c t$
Schnuerer, Oliver, Schulze, Felix, Simon, Miles :
Stability of Euclidean space under Ricci flow, Communictions in Geom. and Ana., Volume 16, Number 1 (2008).
Stability of Euclidean space Ricci flow
Simon, Miles :
Local results for flows whose speed or height satisfies a bound of the form $\frac c t$. International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn097, 14 pages, (2008)
Local results for flows whose speed or height satisfies a bound of the form $\frac c t$
Schnuerer, Oliver, Schulze, Felix, Simon, Miles :
Stability of Euclidean space Ricci flow, Communictions in Geom. and Ana., Volume 16, Number 1 (2008).
Stability of Euclidean space Ricci flow
2007
Simon, Miles :
Ricci flow of almost non-negatively curved three manifolds, accepted 2007: Journal fuer die reine und angewandte Mathematik.
Ricci flow of almost non-negatively curved three manifolds
Simon, Miles :
Ricci flow of almost non-negatively curved three manifolds, accepted 2007: Journal fuer die reine und angewandte Mathematik.
Ricci flow of almost non-negatively curved three manifolds
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)
Deforming Lipschitz metrics into smooth metrics while keeping their curvature operator non-negative
2002
Simon, Miles :
Deformation of C0 Riemannian metrics in the direction of their Ricci curvature, Comm. Anal. Geom. 10 (2002), no. 5, 1033-1074.
Deformation of C0 Riemannian metrics in the direction of their Ricci curvature (with corrections) &
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, (2000), no.1
A class of Riemannian manifolds which pinch when evolved by Ricci flow,