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

Ricci flow does not preserve positive sectional curvature in dimension four [with A. Krishnan] *Submitted.*

arXiv:2112.13291 [math.DG]

Nonplanar minimal spheres in ellipsoids of revolution [with P. Piccione] *Submitted.*

arXiv:2111.14995 [math.DG]

Geography of pinched four-manifolds [with M. Kummer and R. Mendes]
*Submitted.*

arXiv:2106.02138 [math.DG]

# Papers

27. Full Laplace spectrum of distance spheres in symmetric spaces of rank one [with E. Lauret and P. Piccione]* Bull. Lond. Math. Soc., to appear*

arXiv:2012.02349 [math.DG]

26. Global bifurcation for a class of nonlinear ODEs [with P. Piccione] *São Paulo J. Math. Sci., to appear*

arXiv:2107.08181 [math.DG]

25. The first eigenvalue of a homogeneous CROSS [with E. Lauret and P. Piccione] *J. Geom. Anal., to appear*

arXiv:2001.08471 [math.DG] Published version (SpringerLink)

24. Subspace foliations and collapse of closed flat manifolds [with
A. Derdzinski, R. Mossa, and P. Piccione]

*Math. Nachr., to appear*

arXiv:2002.05757 [math.DG]

23. Sectional curvature and Weitzenböck formulae [with R. Mendes]

*Indiana Univ. Math. J., to appear*

arXiv:1708.09033 [math.DG]

22. Convex Algebraic Geometry of Curvature Operators [with M. Kummer and R. Mendes]

*SIAM J. Appl. Algebra Geom., 5 (2021), no. 2, 220-228.* MR4252070

arXiv:1908.03713 [math.DG] Published version (SIAM)

21. Nonuniqueness of conformal metrics with constant Q-curvature [with P. Piccione and Y. Sire]

*Int. Math. Res. Not. IMRN 2021, no. 9, 6967-6992.* MR4251294

arXiv:1806.01373 [math.DG] Published version (Oxford University Press)

20. Instability and bifurcation [with P. Piccione]

*Notices Amer. Math. Soc. 67 (2020), no. 11, 1679-1691.* MR4201907

Published version (Amer. Math. Soc.)

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

*Comm. Anal. Geom. 27 (2019), no. 3, 511-527. * MR4003002

arXiv:1606.00778 [math.DG]
Published version (International Press)

18. Teichmüller theory and collapse of flat manifolds [with A. Derdzinski and P. Piccione],

*Ann. Mat. Pura Appl. (4) 197 (2018), no. 4, 1247-1268.* MR3829569

arXiv:1705.08431 [math.DG]
Published version (SpringerLink)

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

*Ann. Inst. Fourier (Grenoble) 68 (2018), no. 2, 589-609.* MR3803113

arXiv:1603.07788 [math.DG]
Published version

16. Strongly positive curvature [with R. Mendes]

*Ann. Global Anal. Geom. 53 (2018), no. 3, 287-309.* MR3785699

arXiv:1403.2117 [math.DG]
Published version (SpringerLink)

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

*Trans. Amer. Math. Soc., 370 (2018), no. 1, 669-693.* MR3717993

arXiv:1407.4165 [math.DG]
Published version (AMS)

14. Deformations of free boundary CMC hypersurfaces [with P. Piccione and B. Santoro]

*J. Geom. Anal. 27 (2017), no. 4, 3254-3284.* MR3708014

arXiv:1411.0354 [math.DG]
Published version (SpringerLink)

13. Strongly nonnegative curvature [with R. Mendes]

*Math. Ann. 368 (2017), no. 3-4, 971-986.* MR3673642

arXiv:1511.07899 [math.DG] Published version (Open Access, SpringerLink)

12. Four-dimensional manifolds with positive biorthogonal curvature

*Asian J. Math 21 (2017), no. 2, 391-396.* MR3672264

arXiv:1502.02270 [math.DG]
Published version (International Press)

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

* Int. Math. Res. Not. IMRN, 2016, no. 10, 3124-3162.* MR3551832

arXiv:1306.6043 [math.DG] Published version

10. 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

9. 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)

8. 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)

7. 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

6. 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)

5. Positive biorthogonal curvature on $S^2 \times S^2$

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

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

4. 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)

3. 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)

2. 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)

1. 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] Published version (TMNA)

# 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