You can also see the arXiv listing of my preprints.

# Book

Lie Groups and Geometric Aspects of Isometric Actions

[with M. Alexandrino]*Springer 2015, 213 p., hardcover, ISBN 978-3319166124*

Springer.com
Amazon.com

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.

# Preprints

Four-dimensional cohomogeneity one Ricci flow and nonnegative sectional curvature [with A. M. Krishnan], *Submitted.*

arXiv:1606.00778 [math.DG]

Infinitely many solutions to the Yamabe problem on noncompact manifolds [with P. Piccione], *Submitted.*

arXiv:1603.07788 [math.DG]

Strongly nonnegative curvature [with R. Mendes], *Submitted.*

arXiv:1511.07899 [math.DG]

Deformations of free boundary CMC hypersurfaces [with P. Piccione and B. Santoro], *Submitted.*

arXiv:1411.0354 [math.DG]

Strongly positive curvature [with R. Mendes], *Submitted.*

arXiv:1403.2117 [math.DG]

# Papers

Three-manifolds with many flat planes [with B. Schmidt]

*Trans. Amer. Math. Soc., to appear*

arXiv:1407.4165 [math.DG]

Four-dimensional manifolds with positive biorthogonal curvature

*Asian J. Math, to appear*

arXiv:1502.02270 [math.DG]

Delaunay type hypersurfaces in cohomogeneity one manifolds [with P. Piccione]

* Int. Math. Res. Not. IMRN, to appear*

arXiv:1306.6043 [math.DG]

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

Flag manifolds with strongly positive curvature [with R. Mendes]
*Math. Z. 280 (2015), no. 3-4, 1031-1046*. MR3369365, Zbl 06468914.

arXiv:1412.0039 [math.DG]
Published version (SpringerLink)

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)

Equivariant deformations of Hamiltonian stationary Lagrangian submanifolds [with P. Piccione and B. Santoro]

*Mat. Contemp., 43 (2014), 61-88.* MR3426257

arXiv:1302.6970 [math.DG]
Published version

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)

Positive biorthogonal curvature on S^2 x S^2

*Proc. Amer. Math. Soc. 142 (2014), no. 12, 4341-4353.* MR3267002, Zbl 06371055.

arXiv:1210.0043 [math.DG]
Published version (AMS)

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)

Genericity of nondegenerate geodesics with general boundary conditions [with R. Giambò] * Topol. Methods Nonlinear Anal. 35 (2010), no. 2, 339-365.* MR2676821, Zbl 1213.58012.

arXiv:0910.4175 [math.DG]

# Theses

On different notions of positivity of curvature

*Ph.D. Dissertation, Advisor: K. Grove, University of Notre Dame*

PDF
University repository

Generic properties of semi-Riemannian geodesic flows*M.Sc. Thesis, Advisor: P. Piccione, University of São Paulo*

arXiv:1008.4986 [math.DG]
University repository