Research area B: Spaces and Operators
Unit B1: Smooth, singular and rigid spaces in geometry

Research area C: Models and Approximations
Unit C4: Geometry-based modelling, approximation, and reduction

Further Projects
• CRC 1442: Geometry: Deformation and Rigidity - B01: Curvature and Symmetry online
• CRC 1442: Geometry: Deformation and Rigidity - Geometric evolution equations online

Research Interests

$\bullet$ Ricci flow.
$\bullet$ Group actions on Riemannian manifolds.
$\bullet$ Manifolds of positive curvature.
$\bullet$ Singular spaces and convergence of manifolds to singular spaces.

Selected Publications of Prof. Dr. Burkhard Wilking

$\bullet$ M. Radeschi and B. Wilking. On the Berger conjecture for manifolds all of whose geodesics are closed. Invent. Math., 210(3):911–962, 2017.

$\bullet$ E. Cabezas-Rivas and B. Wilking. How to produce a Ricci flow via Cheeger- Gromoll exhaustion. J. Eur. Math. Soc. (JEMS), 17(12):3153–3194, 2015.

$\bullet$ K. Grove and B. Wilking. A knot characterization and 1-connected nonnegatively curved 4-manifolds with circle symmetry. Geom. Topol., 18(5):3091–3110, 2014.

$\bullet$ B. Wilking. A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities. J. Reine Angew. Math., 679:223–247, 2013.

$\bullet$ C. Böhm and B. Wilking. Manifolds with positive curvature operators are space forms. Ann. of Math. (2), 167(3):1079–1097, 2008.

$\bullet$ B. Wilking. A duality theorem for Riemannian foliations in nonnegative sectional curvature. Geom. Funct. Anal., 17(4):1297–1320, 2007.

$\bullet$ C. Böhm and B. Wilking. Nonnegatively curved manifolds with finite fundamental groups admit metrics with positive Ricci curvature. Geom. Funct. Anal., 17(3):665–681, 2007.

$\bullet$ B. Wilking. Positively curved manifolds with symmetry. Ann. of Math. (2), 163(2):607–668, 2006.

$\bullet$ B. Wilking. Torus actions on manifolds of positive sectional curvature. Acta Math., 191(2):259–297, 2003.

$\bullet$ B. Wilking. Manifolds with positive sectional curvature almost everywhere. Invent. Math., 148(1):117–141, 2002.

Current Cluster Publications of Prof. Dr. Burkhard Wilking

$\bullet $ Aaron C. Naber, André A. Neves, and Burkhard Wilking. Geometrie. Oberwolfach Reports, 19(2):1551–1601, April 2023. doi:10.4171/owr/2022/28.

$\bullet $ Lee Kennard, Michael Wiemeler, and Burkhard Wilking. Positive curvature, torus symmetry, and matroids. arXiv e-prints, December 2022. arXiv:2212.08152.

$\bullet $ Claudio Gorodski, Andreas Kollross, and Burkhard Wilking. Actions on positively curved manifolds and boundary in the orbit space. arXiv e-prints, December 2021. arXiv:2112.00513.

$\bullet $ Lee Kennard, Michael Wiemeler, and Burkhard Wilking. Splitting of torus representations and applications in the grove symmetry program. arXiv e-prints, June 2021. arXiv:2106.14723.

$\bullet $ Richard Bamler, Esther Cabezas-Rivas, and Burkhard Wilking. The Ricci flow under almost non-negative curvature conditions. Inventiones Mathematicae, 217:95–126, July 2019. doi:10.1007/s00222-019-00864-7.

$\bullet $ Karsten Grove, Burkhard Wilking, and Joseph Yeager. Almost non-negative curvature and rational ellipticity in cohomogeneity two. Ann. Inst. Fourier, 69(7):2921–2939, January 2019. doi:10.5802/aif.3340.

$\bullet $ Burkhard Wilking and Wolfgang Ziller. Revisiting homogeneous spaces with positive curvature. J. Reine Angew. Math., 738(738):313–328, October 2018. doi:10.1515/crelle-2015-0053.