You can also see the arXiv listing of my preprints.
This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored, keeping a constant connection with the basic material. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries. This book stems from the experience gathered by the authors in several lectures along the years, and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students, and young researchers in geometry, and can be used for a one-semester course or independent study.
Reviews: MR3362465, Zbl 1322.22001.
Four-dimensional manifolds with positive biorthogonal curvature
Asian J. Math, to appear
Bifurcation of periodic solutions to the singular Yamabe problem on spheres [with P. Piccione and B. Santoro]
J. Differential Geom. 103 (2016), no. 2, 191-205. MR3504948
arXiv:1401.7071 [math.DG] Published version
On the equivariant implicit function theorem with low regularity and applications to geometric variational problems [with P. Piccione and G. Siciliano]
Proc. Edinb. Math. Soc., (2) 58 (2015), no. 1, 53-80. MR3333978, Zbl 1317.47057.
arXiv:1009.5721 [math.DG] Published version (Cambridge)
Deforming solutions of geometric variational problems with varying symmetry groups [with P. Piccione and G. Siciliano],
Transform. Groups., 19 (2014), no. 4, 941-968. MR3278856, Zbl 1320.58004.
arXiv:1403.4275 [math.DG] Published version (SpringerLink)
Equivariant bifurcation in geometric variational problems [with P. Piccione and G. Siciliano]
in: Progress in Nonlinear Differential Equations and Their Applications, Vol 85 (2014), 103-133, Springer. MR3330725, Zbl 1321.58010.
arXiv:1308.3268 [math.DG] Published version (SpringerLink)
Multiplicity of solutions to the Yamabe problem on collapsing Riemannian submersions [with P. Piccione]
Pacific J. Math. 266 (2013), no. 1, 1-21. MR3105774, Zbl 1287.53030.
arXiv:1304.5510 [math.DG] Published version (MSP)
Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres [with P. Piccione]
Calc. Var. Partial Differential Equations 47 (2013), no. 3-4, 789–807. MR3070564, Zbl 1272.53042.
arXiv:1107.5335 [math.DG] Published version (SpringerLink)