Research

Fișa de verificare a standardelor minimale CNATDCU (conform OMECTS, Nr. 6129 /20.12.2016)
în domeniul MATEMATICĂ

 

Publications:

Books:

  1. Pintea C.,  Geometry. Elements of Analytic Geometry. Elements of Differentiable Geometry of Curves and Surfaces, (in Romanian),Cluj University Press, Romania, 2001.
  2.  Andrica, D., Pintea, C. Elements of Homotopy Theory with Applications to Critical Points Theory, (in Romanian),  Mirton Publishing House, Timişoara, Romania, 2002.
  3.  Pintea, C., Geometry. Differential Geometry, Riemannian Geometry, Lie groups and Lie Algebras, (in Romanian), Cluj University Press, Romania, 2006.
  4.  Pintea, C., Szöllősi, I., An Introduction to Linear Algebra, Cluj University Press, Romania, 2014.
  5.  Pintea,C., The size of critical and tangency sets, Cluj University Press, Romania, 2021.

Selected papers:

  1. Continuous mappings with an infinite number of topologically critical points. Ann. Polon. Math. 67 (1997), no. 1, 87-93.
  2. A measure of non-immersability of the Grassmann manifolds in some Euclidean spaces, Proc. of the Edinburgh Math. Soc., (41) 1998, 197-206.
  3.  Differentiable mappings with an infinite number of critical points, Proc.Amer. Math. Soc., Vol. 128, no. 11, 2000, 3435-3444.
  4. Closed sets which are not CS∞-critical, Proc. Amer. Math. Soc. 133 (2005), no. 3, 923-930.
  5.  A measure of the deviation from there being fibrations between a pair of compact manifolds, Differential Geom. Appl. 24 (2006), no. 6, 579-587.
  6. Examples of smooth maps with finitely many critical points in dimensions (4,3), (8,5) and (16,9). With L. Funar and P. Zhang. Proc. Amer. Math. Soc. 138 (2010), no. 1, 355-365.
  7. Isomorphic homotopy groups of certain regular sets and their images. With G. Cicortaş  and L. Ţopan. Topology Appl. 157 (2010), no. 3, 635-642.
  8. The size of some critical sets by means of dimension and algebraic φ-category, Topol. Methods Nonlinear Anal. 35 (2010), no. 2, 395-407.
  9.  On preimages of a class of generalized monotone operators. With G. Kassay. Nonlinear Anal. 73 (2010), no. 11, 3537-3545.
  10. Brinkman-type operators on Riemannian manifolds: transmission problems in Lipschitz and C1-domains. With M. Kohr and W. L. Wendland. Potential Anal. 32 (2010), no. 3, 229-273.
  11. Smooth mappings with higher dimensional critical sets, Canad. Math. Bull. 53 (2010), no. 3, 542-549.
  12.  Size of tangencies to non-involutive distributions. With Z. Balogh and H. Rohner. Indiana Univ. Math. J. 60 (2011), no. 6, 2061-2092.
  13. Monotone operators and first category sets. With G. Kassay and S. László. Positivity 16 (2012), no. 3, 565–577.
  14. Global injectivity conditions for planar maps. Monatsh. Math. 172 (2013), no. 3-4, 399-413.
  15. The circular Morse-Smale characteristic of closed surfaces. With D. Andrica and D. Mangra. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 57(105) (2014), no. 3, 235-242.
  16. A class of generalized monotone operators. With D. Marian and I.R. Peter. J. Math. Anal. Appl. 421 (2015), no. 2, 1827-1843.
  17. Operations with monotone operators and the monotonicity of the resulting operators. With D. Marian and I.R. Peter. Monaths. Math. 181(2016), no. 1, 143-168
  18. Necessary conditions for finite critical sets. Maps with infinite critical sets. With I.R. Peter. Topol. Methods Nonlinear Anal., Vol. 47, No. 2, 2016, 739-749.
  19. Closed convex sets of Minkowski type. With Juan Enrique Martinez-Legaz.  J. Math. Anal. Appl. 444 (2016), no. 2, 1195-1202.
  20. The monotonicity of perturbed gradients of convex functions. With T. Trif. J. Convex Anal. 24(2017), no. 2, 525-545.
  21. Manifolds which admit maps with finitely many critical points into spheres of small dimensions, With Louis Funar, Michigan Math. J., 67 (2018), 585-615.
  22. A nonlinear elliptic eigenvalue-transmission problem with Neumann boundary condition. With L. Barbu and Gh. Morosanu, Annali di Matematica Pura ed Applicata (1923-), 198(2019), Issue 3, 821-836.
  23. Convex decompositions of convex open sets with polytopes or finite sets removed,  J. Convex Anal. 26(2019), no. 2.
  24. Convex decompositions and the valence of some functions, With A. Tofan, J. Nonlinear Var. Anal. 4 (2020), No. 2, 225-239.
  25. Closed convex sets with an open or closed Gauss range, With J. E. Martinez-Legaz, Math. Program. 189, 433-454 (2021)
  26. On the Gauss Range of a Closed Convex Set, With J. E. Martinez-Legaz, J. Convex Anal. 30 (2023), No. 4, 1203-1216
  27. Pareto bordered sets,Optimization 73 (2024), no. 11, 3351-3367.
  28. Closed convex sets that are both Motzkin decomposable and generalized Minkowski sets, With  J.E. Martínez-Legaz, J. Nonlinear Var. Anal. 8 (2024), 571-579
  29. Products of functions with bounded Hess+ complement., With A. Brojbeanu, Optimization, (2025)  https://doi.org/10.1080/02331934.2025.2477138.
  30. Conditions for the preservation of Motzkin decomposability and the Pareto bordered property under addition, With B. Moldovan, J. Convex Anal. 32 (2025), no. 4, 1145-1157.
  31. The metric projection over a polyhedral set through the relative interiors of its faces, With V. A. Fodor, Optim. Lett., 19 (2025), 1801-1829.

Research Projects:

     Coordinator of a CNCSIS grant

     Critical points and the  Lusternik-Schnirelmann category. Variational Problems (2007-2008),

      (CNCSIS-competition 2006)

      Team:   Conf. Dr. Cornel Pintea  (Director grant)

                     Prof. Dr. Dorin Andrica 

                     Prof. Dr. Csaba Varga 

                     Conf. Dr. Alexandru Kristály

                     Lect. Dr. Liana Topan

                     Lect. Ildikó-Ilona Mezei  

                     Drd. Ioana-Claudia Lazar