Counterexamples to Calabi conjectures on minimal hypersurfaces ...

[9] L. Jorge and F. Xavier, A complete minimal surface in R 3 between two parallelplanes. Ann. of Math. 112 (1980) 203–206.[10] S. Markvorsen, On the mean exit time from a submanifol. J. DifferentialGeom. 29 (1989), 1-8.[11] F. Martín and S. Morales, A complete bounded minimal cylinder in R 3 .Michigan Math. J. 47 (2000), 499–514.[12] N. Nadirashvili, Hadamard’s and <strong>Calabi</strong>-Yau’s <strong>conjectures</strong> on negativelycurved and minimal surfaces. Invent. Math. 126 (1996), 457–465.[13] S. Pigola, M. Rigoli and A. Setti, A remark on the maximum principle ands<strong>to</strong>chastic completeness. Proc. Amer. Math. Soc. 131 (2003), 1283–1288.[14] S. Pigola, M. Rigoli and A. Setti, Maximum Principle on Riemannian Manifoldsans Applications. Memoirs Amer. Math. Soc. 822 (2005).Luis J. AliasDepartamen<strong>to</strong> de MatematicasUniversidad de MurciaCampus de Espinardo E-30100 – Spainljalias@um.esGregorio Pacelli BessaUFC - Departamen<strong>to</strong> de MatematicaBloco 914 – Campus do Pici60455-760 – Fortaleza – Ceara – Brazilbessa@mat.ufc.brMarcos DajczerIMPAEstrada Dona Cas<strong>to</strong>rina, 11022460-320 – Rio de Janeiro – Brazilmarcos@impa.br10