The Publications of Professor Ehrlich



Books

(1). J. Beem, P. Ehrlich, Global Lorentzian Geometry, Marcel Dekker Pure and Applied Mathematics Volume 67, New York, 1981, 472 pages.

(2). J. Beem, P. Ehrlich, Global Lorentzian Geometry, Mir Publishers, Moscow, 1985, translated into Russian by E. V. Shikin, 400 pages.

(3). P. Ehrlich, J. Beem, K. Easley, Global Lorentzian Geometry, Second Edition, Marcel Dekker Pure and Applied Mathematics Volume 202, New York, 1996, 664 pages.

(4). S. Dostoglou, P. Ehrlich, Advances in Differential Geometry and General Relativity (2003 : Beemfest, University of Missouri- Columbia) , American Mathematical Society Contemporary Mathematics Vol. 359 (2004), 124 pages.

Refereed Publications

(1). J.-P. Bourguignon, P. Ehrlich,"Champs de droites totalement geodesiques a distribution normale integrable et courbure de Ricci", C. R. Acad. Sciences Paris, Serie A, Vol. 279 (4 novembre 1974), pp. 749-752.

(2). P. Ehrlich,"Continuity properties of the injectivity radius function," Compositio Mathematica 29 (1974), pp. 151 - 178.

(3). P. Ehrlich,"Local convex deformations of Ricci and sectional curvature on compact manifolds," Proc. of Symposia in Pure Mathematics, American Mathematical Society 27 (1975), pp. 69 - 71.

(4). P. Ehrlich,"Local convex deformations and sectional curvature," Archiv der Mathematik 26 (1975), pp. 432 - 435.

(5). P. Ehrlich,"A curvature obstruction to covering deformations of connections by metric deformations," Proc. Amer. Math. Soc. 52 (1975), pp. 337 - 342.

(6). P. Ehrlich,"Metric deformations of curvature I: local convex deformations," Geom. Dedicata 5 (1976), pp. 1 - 24.

(7). P. Ehrlich,"Metric deformations of curvature II: compact 3-manifolds," Geom. Dedicata 5 (1976), pp. 147 - 161.

(8). P. Ehrlich,"Deformations of scalar curvature," Geom. Dedicata 5 (1976), pp. 25 - 26.

(9). P. Ehrlich,"Local convex deformations, Hermitian metrics, and Hermitian connections," Geom. Dedicata 5 (1976), pp. 27 - 29.

(10). P. Ehrlich,"Zwei Bemerkungen uber die Ricci-Krummung," Math. Zeitschrift 147 (1976), pp. 29 - 34.

(11). P. Ehrlich, "Conformal deformations and extremal paths in the space of Riemannian metrics," Math. Nachrichten 72 (1976), pp. 137 - 140.

(12). J. Beem, P. Ehrlich,"Conformal deformations, Ricci curvature and energy conditions on globally hyperbolic spacetimes," Proc. Camb. Phil. Soc. 84 (1978), pp. 159 - 175.

(13). J. Beem, P. Ehrlich,"Distance lorentzienne finie et geodesique f-causales incompletes," C. R. Acad. Sci. Paris 285 Series A (19 decembre 1977), pp. 1129 - 1131.

(14). P. Ehrlich, H.-C. Im Hof,"Metric circles and bisectors," Math. Zeitschrift 159 (1978), pp. 101 - 105.

(15). P. Ehrlich, H.-C. Im Hof,"Sur la geometrie de domaines de Dirichlet," C. R. Acad. Sci. Paris 286 Series A (13 mars 1978), pp. 457 - 458.

(16). J. Beem, P. Ehrlich, "Singularities, incompleteness and the Lorentzian distance function," Math. Proc. Camb. Phil. Soc. 85 (1979), pp. 161 - 178.

(17). J. Beem, P. Ehrlich, "The space-time cut locus," Gen. Relativity and Gravitation 11 (1979), pp. 89 - 103.

(18). P. Ehrlich,"Boundary points of the Dirichlet fundamental region," Osaka Math. J. 16 (1979), pp. 439 - 446.

(19). J. Beem, P. Ehrlich,"Cut points, conjugate points and Lorentzian comparison theorems," Math. Proc. Camb. Phil. Soc. 86 (1979), pp. 365 - 384.

(20). J. Beem, P. Ehrlich,"A Morse index theorem for null geodesics," Duke Math. J. 46 (1979), pp. 561 - 569.

(21). P. Ehrlich, H.-C. Im Hof,"Dirichlet regions in manifolds without conjugate points," Commentarii Math. Helv. 54 (1979), pp. 642 - 658.

(22). J. Beem, P. Ehrlich,"Conformal deformations of Ricci curvature on globally hyperbolic manifolds," in Partial Differential Equations and Geometry, ed., C. Byrnes, Marcel Dekker Lecture Notes in Pure and Applied Mathematics, 1979, pp. 5 - 9.

(23). C. Chicone, P. Ehrlich, "Line integration of Ricci curvature and conjugate points on Lorentzian and Riemannian manifolds," Manuscripta Math. 31 (1980), pp. 297 - 316.

(24). J. Beem, P. Ehrlich,"Stability of geodesic incompleteness for Robertson-Walker space-times," Gen. Relativity and Gravitation 13 (1981), pp. 239 - 255.

(25). J. Beem, C. Chicone, P. Ehrlich,"The geodesic flow and sectional curvature of pseudo-Riemannian manifolds," Geom. Dedicata 12 (1982), pp. 111 - 118.

(26). J. Beem, P. Ehrlich,"Constructing maximal geodesics in strongly causal space-times," Math. Proc. Camb. Phil. Soc. 90 (1981), pp. 183 - 190.

(27). J. Beem, P. Ehrlich, "Local extensions and the existence of singularities in General Relativity, Proc. Nagpur Univ. Einstein Centenary Symposium, 1981, pp. 107 - 121.

(28). J. Beem, P. Ehrlich,"Causally disconnecting sets, maximal geodesics, and geodesic incompleteness for strongly causal space-times," Annals of Math. Studies 102 (1982), pp. 499 - 506.

(29). J. Beem, P. Ehrlich, T. Powell, "Warped product manifolds in General Relativity," in "Albert Einstein 1897 - 1955," ed., T. Rassias and G. Rassias, North Holland Publishing Co., Selected Studies: Physics- Astrophysics, Mathematics, History of Science, 1982, pp. 41 - 56.

(30). C. Chicone, P. Ehrlich,"Lorentzian geodesibility," in "Commemorative Volume in Differential Topology, Geometry and Related Fields, and their Applications to the Physical Sciences and Engineering," ed. by G. Rassias, Teubner Text Zur Mathematik, 1985, pp. 75 - 99.

(31). C. Chicone, P. Ehrlich, " Gradient-like and integrable vector fields on |R2 ",Manuscripta Math. 49 (1984), pp. 141 - 164.

(32). J. Beem, P. Ehrlich,"Completeness of timelike and spacelike submanifolds," Colloquia Mathematica Societatis Janos-Bolyai 46 (1984), pp. 137 - 151.

(33). J. Beem, P. Ehrlich, "Timelike isometries of space-times with nonnegative curvature," Colloquia Mathematica Societatis Janos- Bolyai 46 (1984), pp. 153 - 165.

(34). J. Beem, P. Ehrlich,"Incompleteness of timelike submanifolds with nonvanishing second fundamental form," General Relativity and Gravitation 17 (1985), pp. 293 - 300.

(35). J. Beem, P. Ehrlich,"Geodesic completeness of submanifolds in Minkowski space," Geom. Dedicata 18 (1985), pp. 213 - 226.

(36). J. Beem, P. Ehrlich, S. Markvorsen,"A Toponogov splitting theorem for Lorentzian manifolds," Proc. Conference in Global Differential Geometry/ Global Analysis at the Technische Universitat, West Berlin, June, 1984, Springer Verlag Lecture Notes in Mathematics, Vol. 1156 (1985), pp. 1 - 13.

(37). J. Beem, P. Ehrlich, S. Markvorsen, G. Galloway, "Decomposition theorems for Lorentzian manifolds with nonpositive curvature," J. Differential Geometry 22 (1985), pp. 29 - 42.

(38). J. Beem, P. Ehrlich, "Geodesic completeness and stability," Math. Proc. Camb. Phil. Soc. 102 (1987), pp. 319 - 328.

(39). J. Beem, P. Ehrlich, S. Markvorsen, "Timelike isometries and Killing fields," Geom. Dedicata 26 (1988), pp. 247 - 258.

(40). P. Ehrlich, S.-B. Kim, "A Morse index theorem for null geodesics with spacelike endmanifolds," a volume in Geometry and Topology, eds., G. Stratopoulos and G. Rassias, World Scientific Publishing Co. (1989), pp. 105 - 133.

(41). P. Ehrlich, S.-B. Kim,"A focal index theorem for null geodesics," J. Geom. and Physics 6 (1989), pp. 657 - 670.

(42). P. Ehrlich, G. Galloway, "Timelike lines", Classical and Quantum Gravity 7 (1990), pp. 297 - 307.

(43). P. Ehrlich, S.-B. Kim, "A focal Rauch comparison theorem for null geodesics," Communications of the Korean Math. Soc. 6 (1991), pp. 73 - 87.

(44). P. Ehrlich, "Null cones and pseudo-Riemannian metrics," Semigroup Forum 43 (1991), pp. 337 - 343.

(45). P. Ehrlich, G. Emch,"The conjugacy index and simple astigmatic focusing," in Geometry and Nonlinear Partial Differential Equations, eds., V. Oliker and A. Treibergs, Contemporary Mathematics 127 (1992), pp. 27 - 40.

(46). P. Ehrlich, G. Emch, "Gravitational waves and causality," Reviews in Mathematical Physics 4 (1992), pp. 163 - 221.

(47). P. Ehrlich, G. Emch, "Quasi-time functions in Lorentzian geometry," in Geometric Analysis and Partial Differential Equations, ed., I. Bakelman, Marcel Dekker Lecture Notes in Pure and Applied Mathematics 144 (1992), pp. 203 - 232.

(48). P. Ehrlich, G. Emch, "Geodesic and causal behavior of gravitational plane waves: astigmatic conjugacy," Proc. Symposia in Pure Mathematics, Amer. Math. Society 54, Part 2 (1993), pp. 203 - 209.

(49). P. Ehrlich, "Astigmatic conjugacy and achronal boundaries," in Geometry and Global Analysis, Report of the First Mathematical Society of Japan International Research Institute, July 12 - 23, Tohoku University, eds., T. Kotake, S. Nishikawa, R. Schoen, November, 1993, pp. 197 - 208.

(50). P. Ehrlich, S.-B. Kim, "From the Riccati inequality to the Raychaudhuri equation," in Differential Geometry and Mathematical Physics, eds., J. Beem, K. Duggal, Contemporary Mathematics 170 (1994), pp. 65 - 78.

(51). P. Ehrlich, Y.-T. Jung, S.-B. Kim, "Constant scalar curvature on warped product manifolds," Tsukuba Math. J. 20 (1996), pp. 239 - 256.

(52). P. Ehrlich, "The nonspacelike cut locus revisited," Proceedings of the Second World Congress of Nonlinear Analysis, in the journal Nonlinear Analysis, Theory, Methods and Applications 30 (1997), pp. 589 - 596.

(53). P. Ehrlich, Y.-T. Jung, S.-B. Kim, "Volume comparison for Lorentzian manifolds," Geometria Dedicata 73 (1998), pp. 39 - 56.

(54). H. Bahn, P. Ehrlich, "A Brunn-Minkowski Theorem on the Minkowski Spacetime," Canadian J. Math. 51 (1999), pp. 449 - 469.

(55). P. Ehrlich, Y.-T. Jung, S.-B. Kim, C.-H. Shin, "Partial differential equations and scalar curvature of warped product manifolds," Nonlinear Analysis, TMA 44 (2001), pp. 545 - 553.

(56). P. Ehrlich,"Rigidez de curvatura e incompletitud geodesica temporal en la geometria del espacio-tiempo," La Gaceta de la Real Sociedad Matematica Espanola 2 (Mayo - Agosto 1999), pp. 290 - 304.

(57). P. Ehrlich, M. Sanchez,"Some semi-Riemannian volume comparison theorems," Tohoku Mathematics Journal 52 (2000), pp. 331 - 348.

(58). P.Ehrlich, Yoon-Tae Jung, Jeong-Sik Kim, Seon-Bu Kim, "Jacobians and volume comparison for Lorentzian warped products," Contemporary Mathematics 337 (2003), pp. 39 - 52.

(59). P. Ehrlich, K. Easley,"A Beemian Sampler : 1966 - 2002," Contemporary Mathematics 359 (2004), pp. 1 - 29.

(60). P. Ehrlich, S.-B. Kim, "The index form of a warped product," Nonlinear Analysis, Theory, Methods and Applications 63 (2005), pp. e435 - e445.

(61). P. Ehrlich, S.-B. Kim, "Lorentzian Geometry," Encyclopedia of Mathematical Physics, Elsevier, Section 397, 2006.

(62). "A Personal Perspective on Global Lorentzian Geometry," in Analytical and Numerical Approaches to Mathematical Relativity, eds. J. Frauendiener, D. Giulini, V. Perlick, Springer Lecture Notes in Physics 692 (2006), pp. 3 - 34.

(63). P.E. Ehrlich, S.-B. Kim,"Riccati and Index Comparison Methods in Lorentzian and Riemannian Geometry," in Advances in Lorentzian Geometry, eds. M. Plaue, M. Scherfner, Shaker Verlag, Berlin, Germany, 2008, pp. 63 - 76.

(64). Paul E. Ehrlich, Seon-Bu Kim, "Comparison theory in Lorentzian and Riemannian geometry," Nonlinear Analysis 71 (2009), pp. e211 - e217.

Non-Refereed Publications

(1). P. Ehrlich, "The displacement function of a timelike isometry," Sonderforschungsbereich 72 : Approximation und Optimierung, Universitat Bonn, Preprint No. 452 (1981), 19 pages.

(2). P. Ehrlich, "Geodesic completeness of Lorentzian warped product manifolds," in Analysis Seminar Aachen-Bochum-Bonn-Dusseldorf, Sommersemester 1981, Vorlesungsreihe Sonderforschungsbereich 72, No. 8, Bonn University, 1981, pp. 13 - 19.

(3). P. Ehrlich, "The displacement function of a timelike isometry," Tensor N.S. 38 (1982), pp. 29 - 36.

(4). P. Ehrlich, S.-B. Kim, "The index form of a warped product," Isaac Newton Institute Preprint Series, NI05061, manuscript of 14 pages (an extended and improved version of no. 60 above.) see Newton Institute Preprint Series 2005

Miscellaneous

An unpublished manuscript is available on-line in the Department of Mathematics web site and also at the University Archives and University Science Library :

P. Ehrlich (assisted by Nancy Moore),The first sixty-five years: Mathematics at the University of Florida in Gainesville, 1997, 460 pages.

This manuscript discusses the early history of science and engineering at the University of Florida in the early years, then during the later years focuses mostly on the Department of Mathematics.