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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 José 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):23/08567-1 - Pure and Applied Diferential Geometry (PADGE)-2023, AR.EXT
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
+ associated grants 22/13010-3 - Orthogonal geodesics in manifolds with singular boundary. Applications to the theory of minimal surfaces., AV.EXT
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):23/04597-3 - Spectral geometry of embeddings and fibre bundles, BP.PD
22/13818-0 - The Cheeger-Gromoll Splitting Theorem and Applications, BP.MS
22/16298-8 - Enneper Submanifolds of Constant Sectional Curvature, BP.DR
+ associated scholarships 21/10816-4 - Introduction to Riemannian Geometry, BP.IC
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
19/19494-0 - Virtual immersions, isometric immersions of product manifolds and conformal genuine rigidity, BP.PD
19/22488-1 - Some mechanical applications in Riemannian and Finslerian geometry, BP.IC
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

Abstract

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:
Articles published in other media outlets (0 total):
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Scientific publications (37)
(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)
ALEKSEEVSKY, DMITRI; GORODSKI, CLAUDIO. Semisimple symmetric contact spaces. INDAGATIONES MATHEMATICAE-NEW SERIES, v. 31, n. 6, p. 1110-1133, . (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)
DE LIMA, R. F.; MANFIO, F.; DOS SANTOS, J. P.. Hypersurfaces of constant higher-order mean curvature in M x R. Annali di Matematica Pura ed Applicata, v. N/A, p. 50-pg., . (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)
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)
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)
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)
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)
DUSSAN, M. P.; FRANCO FILHO, A. P.; SANTOS, R. S.. Spacelike minimal surfaces which are graphs in R-1(4). Journal of Mathematical Analysis and Applications, v. 519, n. 2, p. 23-pg., . (16/23746-6)
BETTIOL, RENATO G.; PICCIONE, PAOLO. Global bifurcation for a class of nonlinear ODEs. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 16, n. 1, p. 22-pg., . (16/23746-6, 19/09045-3, 19/19891-9)
DE LIMA, R. F.; MANFIO, F.; DOS SANTOS, J. P.. Einstein Hypersurfaces of Warped Product Spaces. Results in Mathematics, v. 77, n. 6, p. 26-pg., . (16/23746-6)
BENCI, VIERI; NARDULLI, STEFANO; PICCIONE, PAOLO; ACEVEDO, LUIS EDUARDO OSORIO. Lusternik-Schnirelman and Morse Theory for the Van der Waals-Cahn-Hilliard equation with volume constraint. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 220, p. 29-pg., . (16/23746-6, 21/05256-0, 17/13155-3, 18/22938-4)
JIMENEZ, M. I.; TOJEIRO, R.. Infinitesimally Bonnet Bendable Hypersurfaces. JOURNAL OF GEOMETRIC ANALYSIS, v. 33, n. 5, p. 17-pg., . (16/23746-6)
CHION, SERGIO; TOJEIRO, RUY. Euclidean Hypersurfaces with Genuine Conformal Deformations in Codimension Two. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, . (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)
GORODSKI, CLAUDIO; GUIMARAES, FELIPPE. The κ-nullity of Riemannian manifolds and their splitting tensors. Annali di Matematica Pura ed Applicata, v. 202, n. 6, p. 23-pg., . (16/23746-6, 19/19494-0)
ALEXANDRINO, MARCOS M.; CARAMELLO JR, FRANCISCO C.. Leaf closures of Riemannian foliations: A survey on topological and geometric aspects of Killing foliations. EXPOSITIONES MATHEMATICAE, v. 40, n. 2, p. 54-pg., . (18/14980-0, 16/23746-6)
BETTIOL, RENATO G.; LAURET, EMILIO A.; PICCIONE, PAOLO. Full Laplace spectrum of distance spheres in symmetric spaces of rank one. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, v. N/A, p. 22-pg., . (19/09045-3, 16/23746-6)
JIMENEZ, M. I.; TOJEIRO, R.. Umbilical submanifolds of H-k X Sn-k+1. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 81, p. 19-pg., . (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)
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)
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)
GOMES, ANDRE MAGALHAES DE SA; GORODSKI, CLAUDIO. REPRESENTATIONS OF LOW COPOLARITY. Proceedings of the American Mathematical Society, v. 150, n. 12, p. 9-pg., . (16/23746-6)
DUSSAN, M. P.; FRANCO FILHO, A. P.; MAGID, M.. Timelike surfaces in the de Sitter space S-1(3) (1) subset of R-1(4). ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v. 61, n. 4, p. 20-pg., . (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)
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)
GORODSKI, CLAUDIO. Highly curved orbit spaces. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 63, p. 145-165, . (16/23746-6)
LOBOS, GUILLERMO; MELARA, MYNOR; PALMAS, OSCAR. Pseudo-parallel Lorentzian Surfaces in Pseudo-Riemannian Space Forms. Results in Mathematics, v. 78, n. 2, p. 30-pg., . (16/23746-6)
BETTIOL, RENATO G.; DERDZINSKI, ANDRZEJ; MOSSA, ROBERTO; PICCIONE, PAOLO. Subspace foliations and collapse of closed flat manifolds. Mathematische Nachrichten, v. 295, n. 12, p. 19-pg., . (19/19891-9, 19/16286-7, 16/23746-6, 18/08971-9)
CHION, SERGIO; TOJEIRO, RUY. Euclidean Hypersurfaces with Genuine Conformal Deformations in Codimension Two. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 51, n. 3, p. 54-pg., . (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, v. 199, n. 6, p. 29-pg., . (16/23746-6)
ALEXANDRINO, MARCOS M.; CAVENAGHI, LEONARDO F.; GONCALVES, ICARO. On mean curvature flow of singular Riemannian foliations: Noncompact cases. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 72, p. 18-pg., . (17/24680-1, 16/23746-6)

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