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Algebraic, topological and analytical techniques in differential geometry and geometric analysis

Grant number: 16/23746-6
Support Opportunities:Research Projects - Thematic Grants
Duration: July 01, 2017 - June 30, 2023
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 ; Francesco Mercuri ; Marcos Martins Alexandrino da Silva ; Ruy Tojeiro de Figueiredo Junior
Associated researchers:Alexandre Paiva Barreto ; Ana Cláudia da Silva Moreira ; André Salles de Carvalho ; Cristián Andrés Ortiz González ; Dirk Toeben ; Fábio Armando Tal ; Fernando Manfio ; Francisco Jose Gozzi ; Gaetano Siciliano ; Glaucio Terra ; Guillermo Antonio Lobos Villagra ; Ivan Struchiner ; Llohann Dallagnol Sperança ; Luiz Roberto Hartmann Junior ; Martha Patricia Dussan Angulo ; Patricia Romano Cirilo ; Pedro Paiva Zühlke d'Oliveira
Associated grant(s):22/16384-1 - Connections with Prescribed Curvature via Poisson Geometry, AV.EXT
22/14254-3 - Geometric dynamics between São Paulo and New York, AP.R SPRINT
22/13010-3 - Orthogonal geodesics in manifolds with singular boundary. Applications to the theory of minimal surfaces., AV.EXT
+ associated grants 19/19891-9 - Minimal spheres in ellipsoids, AV.EXT
19/16286-7 - Topics on curved and flat manifolds, AP.R SPRINT
19/23370-4 - Symmetry and Shape, AR.EXT
19/09045-3 - Geometry and dynamics between São Paulo and New York, AP.R SPRINT
19/12180-0 - Four topics on curved and flat manifolds, AV.EXT
17/22098-3 - Moduli space of flat metrics, AV.EXT
17/26597-4 - 20th School of Differential Geometry, AR.BR
17/22091-9 - Cohomology of Lie algebroids in the holomorphic and algebraic settings: theory and applications, AV.EXT - associated grants
Associated scholarship(s):22/13818-0 - The Cheeger-Gromoll Splitting Theorem and Applications, BP.MS
22/16298-8 - Enneper Submanifolds of Constant Sectional Curvature, BP.DR
21/10816-4 - Introduction to Riemannian Geometry, BP.IC
+ associated scholarships 21/03304-7 - Enneper surfaces, BP.MS
21/05766-8 - Complete surfaces in homogeneous spaces with constant mean curvature, BP.MS
21/03599-7 - From geometric analysis to bifurcation, BP.PD
20/13512-3 - A topological and dynamical approach to Fractal Geometry, BP.MS
21/00551-3 - Finsler distance function and wavefronts, BP.IC
20/07566-3 - Qualitative properties for higher order and non-local PDEs arising in Differential Geometry, BP.PD
19/20789-4 - Deformations of geometric structures and Lie groupoids, BP.PD
20/12018-5 - Higher Structures in Geometry and Mathematical Physics, BP.PD
20/03431-6 - Uniqueness of immersed spheres in three-dimensional Riemannian manifolds and Enneper-type hypersurfaces, BP.PD
19/26177-0 - Complete real Kaehler submanifolds, BP.PD
19/14777-3 - The interplay between Lie groupoids and Riemannian Geometry, BP.PD
19/16142-5 - Classification of surfaces, BP.IC
19/22488-1 - Some mechanical applications in Riemannian and Finslerian geometry, BP.IC
19/19494-0 - Virtual immersions, isometric immersions of product manifolds and conformal genuine rigidity, BP.PD
19/18940-6 - Geometric applications of the maximum principle, BP.IC
19/04344-2 - Embedded minimal surfaces in R^3, BP.IC
19/04027-7 - Submanifolds of codimension two with constant Moebius curvature and flat normal bundle, BP.DR
18/14980-0 - Geometry and topology of Riemannian foliations via deformations, BP.PD
17/24680-1 - Metric deformations and applications, BP.DR
17/22704-0 - Bifurcation in geometric variational problems, BP.DR - associated scholarships


The projets addresses several topics in differential geometry and geometric analysis, including: 1) group and groupoid actions in riemannian and pseudo-riemannian manifolds; 2) submanifold theory, minimal submanifolds and constant mean curvature hypersurfaces; 3) variational calculus and global analysis in riemannian, sub-riemannian and pseudo-riemannian geometry, with applications to general relativity; 4) Lusternik-Schnirelman Theory, Morse Theory; 5) geometric variational problems and PDEs on manifolds; 6) isometric immersions in riemannian and pseudo-riemannian manifolds; 7) geometric theory of foliations; 8) Lie groupoids and algebroids, Poisson and Dirac geometry, G-structures; 9) Finsler and pseudo-Finsler manifolds. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications (20)
(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)
DO REI FILHO, C.; TOJEIRO, R.. Conformally flat hypersurfaces with constant scalar curvature. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 61, p. 133-146, . (16/23746-6)
BEZERRA, A. C.; MANFIO, F.. Rigidity and stability estimates for minimal submanifolds in the hyperbolic space. Journal of Mathematical Analysis and Applications, v. 495, n. 2, . (16/23746-6)
CANEVARI, SAMUEL; DE FREITAS, GUILHERME MACHADO; GUIMARAES, FELIPPE; MANFIO, FERNANDO; DOS SANTOS, JOAO PAULO. Complete submanifolds with relative nullity in space forms. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v. 59, n. 1, p. 81-92, . (19/19494-0, 16/23746-6)
LOBOS, G. A.; TASSI, M. P.. A classification of pseudo-parallel hypersurfaces of S-n x R and H-n x R. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 62, p. 72-82, . (16/23746-6)
LOBOS, G. A.; TASSI, M. P.; YUCRA HANCCO, A. J.. Pseudo-parallel surfaces of S-c(n) x R and H-c(n) x R. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 50, n. 3, p. 705-715, . (16/23746-6)
BETTIOL, RENATO G.; LAURET, EMILIO A.; PICCIONE, PAOLO. The First Eigenvalue of a Homogeneous CROSS. JOURNAL OF GEOMETRIC ANALYSIS, v. 32, n. 3, . (19/19891-9, 19/09045-3, 16/23746-6)
CANEVARI, S.; TOJEIRO, RUY. Isometric immersions of space forms into S-p x R. Mathematische Nachrichten, v. 293, n. 7, p. 1259-1277, . (16/23746-6)
ALEKSEEVSKY, DMITRI; GORODSKI, CLAUDIO. Semisimple symmetric contact spaces. INDAGATIONES MATHEMATICAE-NEW SERIES, v. 31, n. 6, p. 1110-1133, . (16/23746-6)
DAJCZER, MARCOS; TOJEIRO, RUY. Hypersurfaces of space forms carrying a totally geodesic foliation. Geometriae Dedicata, v. 205, n. 1, p. 129-146, . (16/23746-6)
MANFIO, FERNANDO; TOJEIRO, RUY; VAN DER VEKEN, JOERI. Geometry of submanifolds with respect to ambient vector fields. Annali di Matematica Pura ed Applicata, . (16/23746-6)
ALEXANDRINO, MARCOS M.; ALVES, BENIGNO O.; DEHKORDI, HENGAMEH R.. On Finsler transnormal functions. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 65, p. 93-107, . (16/23746-6)
GORODSKI, CLAUDIO; MENDES, RICARDO A. E.; RADESCHI, MARCO. Robust index bounds for minimal hypersurfaces of isoparametric submanifolds and symmetric spaces. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 58, n. 4, . (16/23746-6)
GORODSKI, CLAUDIO. Highly curved orbit spaces. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 63, p. 145-165, . (16/23746-6)
DO REI FILHO, C.; TOJEIRO, R.. Minimal Conformally Flat Hypersurfaces. JOURNAL OF GEOMETRIC ANALYSIS, v. 29, n. 3, p. 2931-2956, . (16/23746-6)
ALEXANDRINO, MARCOS M.; ALVES, BENIGNO O.; ANGEL JAVALOYES, MIGUEL. On singular Finsler foliation. Annali di Matematica Pura ed Applicata, v. 198, n. 1, p. 205-226, . (16/23746-6, 11/21362-2)
CHION, SERGIO; TOJEIRO, RUY. Euclidean Hypersurfaces with Genuine Conformal Deformations in Codimension Two. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, . (16/23746-6)
ALEXANDRINO, MARCOS M.; INAGAKI, MARCELO K.; DE MELO, MATEUS; STRUCHINER, IVAN. ie groupoids and semi-local models of singular Riemannian foliation. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v. 61, n. 3, p. 593-619, . (15/22059-2, 19/14777-3, 16/23746-6)
DUSSAN, M. P.; FRANCO FILHO, A. P.; SIMOES, P.. Spacelike Surfaces in L-4 with null mean curvature vector and the nonlinear Riccati partial differential equation. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 207, . (16/23746-6)
LIU, ZHISU; SICILIANO, GAETANO. A perturbation approach for the Schrodinger-Born-Infeld system: Solutions in the subcritical and critical case. Journal of Mathematical Analysis and Applications, v. 503, n. 2, . (18/17264-4, 19/27491-0, 16/23746-6)

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