Modern methods in differential geometry and geometric analysis

• Grant number: 22/16097-2
• Support Opportunities: Research Projects - Thematic Grants
• Start date: July 01, 2023
• End date: June 30, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paolo Piccione
• Grantee: Paolo Piccione
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Pesquisadores principais: Claudio Gorodski ; Marcos Martins Alexandrino da Silva ; Ruy Tojeiro de Figueiredo Junior
• Associated researchers: Alexandre Paiva Barreto ; Ana Cláudia da Silva Moreira ; Cristián Andrés Ortiz González ; Dirk Toeben ; Fábio Armando Tal ; Fernando Manfio ; Francesco Mercuri ; Francisco José Gozzi ; Gaetano Siciliano ; Guillermo Antonio Lobos Villagra ; Hengameh Raeisidehkordi ; Henrique Nogueira de Sá Earp ; Ivan Struchiner ; João Henrique Santos de Andrade ; José Nazareno Vieira Gomes ; Lino Anderson da Silva Grama ; Luiz Roberto Hartmann Junior ; Marcos Benevenuto Jardim ; Patricia Romano Cirilo ; Stefano Nardulli
• Associated research grant(s): 25/13237-6 - Orbit spaces, leaf spaces and minimal hypersurfaces in symmetric spaces, AV.EXT; 25/01840-0 - A priori estimates for solutions of certain elliptic quasi-linear PDEs, with applications to Geometric Analysis, AV.BR; 24/22850-0 - Finsler spacetimes and Zermelo foliations, AV.EXT; 23/16527-0 - XI International Meeting on Lorentzian Geometry, AR.EXT; 23/00635-8 - Geometry in Muenster and São Paulo, AP.R SPRINT
• Associated scholarship(s): 25/13518-5 - Representations of compact Lie groups and their orbit spaces, BP.DR; 25/00282-3 - Hypersurfaces of Symmetric Spaces, Biquotients and Orbifolds, BP.DR; 24/22841-1 - Lie groupoids of symmetries and geometric structures on manifolds, BP.PD; + associated scholarships 25/00281-7 - Totally geodesic submanifolds in homogeneous spaces, BP.DR; 24/14883-6 - Geometry of algebraic curvature operators, BP.PD; 24/06702-1 - Geometry of interconnected mechanical systems, BP.IC; 24/03493-2 - On isometric rigidity, BP.PD; 24/03446-4 - Submanifolds and Submersions in Finsler Geometry, BP.PD; 24/01929-8 - Ricci flow min model geometries, BP.DR; 23/13921-9 - Mean curvature solitons in an extended Ricci flow background, BP.PD; 23/14796-3 - Free Boundary Minimal Submanifolds in Euclidean Balls and Ricci Surfaces, BP.PD - associated scholarships

Abstract

The researchers and students participating in this project to investigate new trends regarding differential geometric methods used in modern theories of Mathematics and Physics. The project program combines research in differential geometry and geometric analysis. Transcending the boundaries of the associated subprojects are a range of modern techniques such as geometric flows, PDE solution bifurcations, calibrations, group actions (symmetries), foliations and Hamiltonian dynamics. Individual projects are foreseen, as well as research activities coordinated with groups. These activities will favor a coherence of research directions, identifying promising lines of interdisciplinary research, and will encourage the establishment of new scientific collaborations. (AU)

Scientific publications

(10)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

LOBOS, GUILLERMO A.; MELARA, MYNOR; SANTOS, MARIA R. B.. A Simons Type Formula for Spacelike Submanifolds in Semi-Riemannian Warped Product and its Applications. Results in Mathematics, v. 79, n. 8, p. 22-pg., 2024-12-01. (22/16097-2)

CAPONIO, ERASMO; CORONA, DARIO; GIAMBO, ROBERTO; PICCIONE, PAOLO. Fixed energy solutions to the Euler-Lagrange equations of an indefinite Lagrangian with affine Noether charge. Annali di Matematica Pura ed Applicata, v. 203, n. 4, p. 32-pg., 2024-04-23. (22/13010-3, 22/16097-2)

JIANG, QIAOYUN; LI, LIN; CHEN, SHANGJIE; SICILIANO, GAETANO. GROUND STATE SOLUTIONS FOR NONLINEAR SCHRODINGER-BOPP-PODOLSKY BOPP-PODOLSKY SYSTEMS WITH NONPERIODIC POTENTIALS. Electronic Journal of Differential Equations, v. 2024, n. 43, p. 25-pg., 2024-08-12. (22/16097-2, 22/16407-1)

RAMOS, GUSTAVO DE PAULA; SICILIANO, GAETANO. Existence and Concentration of Semiclassical Bound States for a Quasilinear Schrodinger-Poisson System. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, v. 47, n. 6, p. 26-pg., 2024-11-01. (22/16097-2, 22/16407-1)

CORONA, D.; NARDULLI, S.; OLIVER-BONAFOUX, R.; ORLANDI, G.; PICCIONE, P.. Multiplicity results for mass constrained Allen-Cahn equations on Riemannian manifolds with boundary. MATHEMATISCHE ANNALEN, v. N/A, p. 46-pg., 2025-05-07. (22/13010-3, 23/08246-0, 21/05256-0, 22/16097-2)

MANFIO, F.; DOS SANTOS, J. B. M.; DOS SANTOS, J. P.; VAN DER VEKEN, J.. Hypersurfaces of S3 x Rand H3 x R with constant principal curvatures. JOURNAL OF GEOMETRY AND PHYSICS, v. 213, p. 9-pg., 2025-04-10. (22/16097-2)

GARCIA, ESTELA; MANFIO, FERNANDO. Einstein submanifolds with parallel mean curvature vector field into SnxR. JOURNAL OF GEOMETRY, v. 116, n. 2, p. 16-pg., 2025-08-01. (22/16097-2)

ANTAS, M. S. R.; TOJEIRO, R.. Submanifolds with constant Moebius curvature and flat normal bundle. MANUSCRIPTA MATHEMATICA, v. 174, n. 3-4, p. 32-pg., 2024-04-01. (22/16097-2, 19/04027-7)

JIMENEZ, M. I.; TOJEIRO, R.. Infinitesimally Moebius bendable hypersurfaces. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 67, n. 1, p. 25-pg., 2024-01-11. (22/16097-2, 22/05321-9)

PICCIONE, PAOLO; YANG, MINBO; ZHAO, SHUNNENG. Quantitative profile decomposition and stability for a nonlocal Sobolev inequality. Journal of Differential Equations, v. 417, p. 41-pg., 2025-02-05. (22/16097-2)