Frederico Xavier

Emeritus - Full

Education

B.S., University of Pernambuco, 1971
M.S., University of Pernambuco, 1973
Ph.D., University of Rochester, 1977

Research Groups

Analysis and Partial Differential Equations, Differential Geometry, Mathematical Physics

Research Area

Differential Geometry and Geometric Analysis

Bio

Research Interests

Differential geometry, geometric analysis.

Selected Publications

  • F. Xavier (with L. P.Jorge), A complete minimal surface between two parallel planes, Annals of Mathematics, 112 (1980), 203–-206.
  • F. Xavier, The Gauss map of complete minimal surface cannot omit 7 points of the sphere,_ Annals of Mathematics,_ 113 (1981) (erratum on v.115, 211–-214).
  • F.  Xavier (with H. Donnelly), On the differential form spectrum of negatively  curved manifolds,  _American Journal of Mathematics,_ 106 (1984), 169–-187.
  • F.  Xavier (with B. Smyth), Efimov’s theorem in dimension greater than two, Invent. Math. 90 (l987), 443-450.
  • F.  Xavier (with B. Smyth), Injectivity of local diffeomorphisms from nearly  spectral conditions,  _Jour. Diff. Eq.,_ vol. 130, No. 2, 406-414 (1996).
  • F. Xavier (with J. Cao),  Kahler parabolicity and the Euler number of compact manifolds of non-positive curvature, Math. Ann., 319, 483 — 491 (2001).
  • F. Xavier (with S. Nollet), Holomorphic Injectivity and the Hopf map, Geometric and Functional Analysis  (GAFA) 14, No. 6 (2004) 1339-1351.
  • F. Xavier, Using Gauss maps  to detect intersections,  _L’Enseignement Mathematique,_ 53, 15-31, 2007.
  • F. Xavier, Rigidity of the Identity, _Comm. Cont. Math,_ 9, 691-699, 2007.
  • F. Xavier (with S. Nollet, L. Taylor ), Birationality of etale maps via surgery,  _J. reigne angew._ Math. 627 (2009), 83-95.

Email: fxavier@nd.edu
Office: 161 Hurley Hall