Ehrlich, Paul Ewing

• 2671829
  Ehrlich, Paul E.(1-FL); Kim, Seon-Bu(KR-CHON)
  Comparison theory in Lorentzian and Riemannian geometry. (English summary)
  Nonlinear Anal. 71 (2009), no. 12, e211--e217.
  53Cxx
  
• 2582613
  Ehrlich, Paul E.(1-FL); Kim, Jong Ryul(KR-CHON); Kim, Seon-Bu(KR-CHON)
  Nonisolated spacelike focal and conjugate points in Lorentzian geometry. (English summary)
  J. Math. Phys. 50 (2009), no. 12, 123517, 11 pp.
  53C50
  
• 2603187
  Ehrlich, Paul E.(1-FL); Kim, Seon-Bu(KR-CHON)
  Riccati and index comparison methods in Lorentzian and Riemannian geometry. (English summary) Advances in Lorentzian geometry, 63--75, Shaker Verlag, Aachen, 2008.
  58Exx (53Cxx)
  
• 2222545
  Ehrlich, Paul E.(1-FL)
  A personal perspective on global Lorentzian geometry. (English. English summary)
  Analytical and numerical approaches to mathematical relativity, 3--34,
  Lecture Notes in Phys., 692,
  Springer, Berlin, 2006.
  53C50
• 2096150
  Ehrlich, Paul E.(1-FL); Easley, Kevin L.(1-TRU)
  A Beemian sampler: 1966--2002. (English. English summary)
  Advances in differential geometry and general relativity, 1--29,
  Contemp. Math., 359,
  Amer. Math. Soc., Providence, RI, 2004.
  53-02 (83-02)
• 2094088
  Advances in differential geometry and general relativity.
  Papers from the Beemfest on the occasion of Professor John Beem's retirement held at the University of Missouri-Columbia, Columbia, MO, May 10--11, 2003. Edited by S. Dostoglou and P. Ehrlich. Contemporary Mathematics, 359.
  American Mathematical Society, Providence, RI, 2004. xii+124 pp. ISBN 0-8218-3539-4
  53-06 (83-06)
• 2040467
  Ehrlich, Paul E.(1-FL); Jung, Yoon-Tae(KR-CHS); Kim, Jeong-Sik(KR-CHON); Kim, Seon-Bu(KR-CHON)
  Jacobians and volume comparison for Lorentzian warped products. (English. English summary)
  Recent advances in Riemannian and Lorentzian geometries (Baltimore, MD, 2003), 39--52,
  Contemp. Math., 337,
  Amer. Math. Soc., Providence, RI, 2003.
  53C50
• 1822102
  Ehrlich, Paul E.(1-FL); Jung, Yoon-Tae(KR-CHS); Kim, Seon-Bu(KR-CHON); Shin, Cheol-Guen
  Partial differential equations and scalar curvature of warped product manifolds.
  Nonlinear Anal. 44 (2001), no. 4, Ser. A: Theory Methods, 545--553.
  53C21
• 1772801
  Ehrlich, Paul E.(1-FL); Sánchez, Miguel(E-GRANS-GT)
  Some semi-Riemannian volume comparison theorems. (English. English summary)
  Tohoku Math. J. (2) 52 (2000), no. 3, 331--348.
  53C50 (53C20 53C21)
• 1750194
  Ehrlich, Paul(1-FL)
  Rigidity of curvature and temporal geodesic incompleteness in the geometry of space-time. (Spanish)
  Gac. R. Soc. Mat. Esp. 2 (1999), no. 2, 290--304.
  53C50 (53C24 83C99)
• 1701320
  Bahn, Hyoungsick(KR-POST); Ehrlich, Paul(1-FL)
  A Brunn-Minkowski type theorem on the Minkowski spacetime. (English. English summary)
  Canad. J. Math. 51 (1999), no. 3, 449--469.
  53B30 (52A38 52A40)
• 1651891
  Ehrlich, Paul E.(1-FL); Jung, Yoon-Tae(KR-CHS); Kim, Seon-Bu(KR-CHON)
  Volume comparison theorems for Lorentzian manifolds. (English. English summary)
  Geom. Dedicata 73 (1998), no. 1, 39--56.
  53C50 (53C20)
• 1489825
  Ehrlich, Paul(1-FL)
  The nonspacelike cut locus revisited.
  Proceedings of the Second World Congress of Nonlinear Analysts, Part 1 (Athens, 1996).
  Nonlinear Anal. 30 (1997), no. 1, 589--596.
  53C50
• 1406047
  Ehrlich, Paul E.(1-FL); Jung, Yoon-Tae(KR-CHS); Kim, Seon-Bu(KR-CHON)
  Constant scalar curvatures on warped product manifolds.
  Tsukuba J. Math. 20 (1996), no. 1, 239--256.
  53C21 (53C50)
• 1384756
  Beem, John K.(1-MO); Ehrlich, Paul E.(1-FL); Easley, Kevin L.(1-TRU)
  Global Lorentzian geometry. (English. English summary)
  Second edition. Monographs and Textbooks in Pure and Applied Mathematics, 202.
  Marcel Dekker, Inc., New York, 1996. xiv+635 pp. ISBN 0-8247-9324-2
  53C50 (53-02 83-02)
• 1290565
  Ehrlich, Paul E.(1-FL); Kim, Seon-Bu(KR-CHON)
  From the Riccati inequality to the Raychaudhuri equation. (English. English summary)
  Differential geometry and mathematical physics (Vancouver, BC, 1993), 65--78,
  Contemp. Math., 170,
  Amer. Math. Soc., Providence, RI, 1994.
  53C50 (53C20)
• 1361182
  Ehrlich, Paul E.(1-FL)
  Astigmatic conjugacy and achronal boundaries.
  Geometry and global analysis (Sendai, 1993), 197--208,
  Tohoku Univ., Sendai, 1993.
  53C50
• 1216540
  Ehrlich, Paul E.(1-FL); Emch, Gérard G.(1-FL)
  Geodesic and causal behavior of gravitational plane waves: astigmatic conjugacy.
  Differential geometry: geometry in mathematical physics and related topics (Los Angeles, CA, 1990), 203--209,
  Proc. Sympos. Pure Math., 54, Part 2,
  Amer. Math. Soc., Providence, RI, 1993.
  53C50 (53C80 83C35 83C75)
• 1207183
  Ehrlich, Paul E.(1-FL); Emch, Gérard G.(1-FL)
  Quasi-time functions in Lorentzian geometry.
  Geometric analysis and nonlinear partial differential equations (Denton, TX, 1990), 203--212,
  Lecture Notes in Pure and Appl. Math., 144,
  Dekker, New York, 1993.
  53C50 (83C99)
• 1189120
• 1174246
• 1155407
  Ehrlich, Paul E.(1-FL); Emch, Gérard G.(1-FL)
  The conjugacy index and simple astigmatic focusing.
  Geometry and nonlinear partial differential equations (Fayetteville, AR, 1990), 27--39,
  Contemp. Math., 127,
  Amer. Math. Soc., Providence, RI, 1992.
  53C50 (53C22 83C35)
• 1125065
  Ehrlich, Paul(1-FL)
  Null cones and pseudo-Riemannian metrics.
  Semigroup Forum 43 (1991), no. 3, 337--343.
  53B30 (53C50 53C80)
• 1038611
  Ehrlich, Paul E.(1-FL); Galloway, Gregory J.(1-FL)
  Timelike lines.
  Classical Quantum Gravity 7 (1990), no. 3, 297--307.
  53C50 (53C80 83C75)
• 1076707
  Ehrlich, Paul E.(1-FL); Kim, Seon-Bu(KR-CHON)
  A focal index theorem for null geodesics.
  J. Geom. Phys. 6 (1989), no. 4, 657--670.
  53C50 (53C22)
• 1001592
  Ehrlich, Paul E.(1-FL); Kim, Seon-Bu(KR-CHON)
  A Morse index theorem for null geodesics with spacelike endmanifolds.
  Geometry and topology, 105--133,
  World Sci. Publishing, Singapore, 1989.
  53C50 (53C22 58E10)
• 950063
  Beem, John K.(1-MO); Ehrlich, Paul E.(1-MO); Markvorsen, Steen(DK-TUD)
  Timelike isometries and Killing fields.
  Geom. Dedicata 26 (1988), no. 3, 247--258.
  53C50
• 933841
  Beem, J. K.(1-MO); Ehrlich, P. E.(1-MO); Markvorsen, S.(DK-TUD)
  Timelike isometries of space-times with nonnegative sectional curvature.
  Topics in differential geometry, Vol. I, II (Debrecen, 1984), 153--165,
  Colloq. Math. Soc. János Bolyai, 46,
  North-Holland, Amsterdam, 1988.
  53C50 (53C22)
• 933840
  Beem, J. K.(1-MO); Ehrlich, P. E.(1-MO)
  Completeness of timelike and spacelike submanifolds.
  Topics in differential geometry, Vol. I, II (Debrecen, 1984), 137--151,
  Colloq. Math. Soc. János Bolyai, 46,
  North-Holland, Amsterdam, 1988.
  53C50 (53C22)
• 898152
  Beem, John K.(1-MO); Ehrlich, Paul E.(1-MO)
  Geodesic completeness and stability.
  Math. Proc. Cambridge Philos. Soc. 102 (1987), no. 2, 319--328.
  53C50 (53C22)
• 836533
  Bim, Dzh.(1-MO); Èrlikh, P.(1-MO)
  {\cyr Global\cprime naya Lorentseva geometriya}. (Russian) [Global Lorentzian geometry]
  Translated from the English and with a preface by E. V. Shikin.
  ``Mir'', Moscow, 1985. 400 pp.
  53C50 (53-02)
• 827987
  Chicone, Carmen(1-MO); Ehrlich, Paul(1-MO)
  Lorentzian geodesibility.
  Differential topology-geometry and related fields, and their applications to the physical sciences and engineering, 75--99,
  Teubner-Texte Math., 76,
  Teubner, Leipzig, 1985.
  53C50 (58F17)
• 826422
• 824057
• 792582
  Beem, John K.(1-MO); Ehrlich, Paul E.(1-MO)
  Geodesic completeness of submanifolds in Minkowski space.
  Geom. Dedicata 18 (1985), no. 2, 213--226.
  53C50 (53C40)
• 787299
  Beem, John K.(1-MO); Ehrlich, Paul E.(1-MO)
  Incompleteness of timelike submanifolds with nonvanishing second fundamental form.
  Gen. Relativity Gravitation 17 (1985), no. 3, 293--300.
  53C50
• 767203
  Chicone, Carmen(1-MO); Ehrlich, Paul(1-MO)
  Gradient-like and integrable vector fields on $ R\sp 2$.
  Manuscripta Math. 49 (1984), no. 2, 141--164.
  58F05 (58F15)
• 832621
  Ehrlich, Paul E.(1-MO)
  The displacement function of a timelike isometry.
  Tensor (N.S.) 38 (1982), 29--36.
  53C50
• 648686
  Beem, J.; Chicone, C.; Ehrlich, P.
  The geodesic flow and sectional curvature of pseudo-Riemannian manifolds.
  Geom. Dedicata 12 (1982), no. 2, 111--118.
  53B30 (53C50 58F17)
• 662851
  Beem, J. K.; Ehrlich, P. E.; Powell, Th. G.
  Warped product manifolds in relativity.
  Selected studies: physics-astrophysics, mathematics, history of science, pp. 41--56,
  North-Holland, Amsterdam-New York, 1982.
  53C50 (83C99)
• 611293
  Beem, John K.; Ehrlich, Paul E.
  Constructing maximal geodesics in strongly causal space-times.
  Math. Proc. Cambridge Philos. Soc. 90 (1981), no. 1, 183--190.
  53C50 (53C22 83C99)
• 627796
  Beem, John K.; Ehrlich, Paul E.
  Stability of geodesic incompleteness for Robertson-Walker space-times.
  Gen. Relativity Gravitation 13 (1981), no. 3, 239--255.
  83C99 (53B30)
• 619853
  Beem, John K.; Ehrlich, Paul E.
  Global Lorentzian geometry.
  Monographs and Textbooks in Pure and Applied Math., 67.
  Marcel Dekker, Inc., New York, 1981. vi+460 pp. ISBN 0-8247-1369-9
  53C50 (53-02 83-02)
• 673612
  Beem, John K.; Ehrlich, Paul E.
  Local extensions and the existence of singularities in general relativity.
  Proceedings of Einstein Centenary Symposium, Vol. I (Nagpur, 1980), pp. 107--121,
  Duhita, Nagpur, 1980.
  53C50 (51B20 83C99)
• 576502
  Chicone, Carmen; Ehrlich, Paul
  Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds.
  Manuscripta Math. 31 (1980), no. 1-3, 297--316.
  53C50 (83C99)
• 552837
  Beem, John K.; Ehrlich, Paul E.
  The space-time cut locus.
  Gen. Relativity Gravitation 11 (1979), no. 2, 89--103.
  53C50 (83C99)
• 552682
  Ehrlich, Paul E.; Im Hof, Hans-Christoph
  Dirichlet regions in manifolds without conjugate points.
  Comment. Math. Helv. 54 (1979), no. 4, 642--658.
  53C20 (57R99)
• 544246
  Beem, John K.; Ehrlich, Paul E.
  A Morse index theorem for null geodesics.
  Duke Math. J. 46 (1979), no. 3, 561--569.
  53C50 (53B30)
• 539599
  Ehrlich, Paul E.
  Boundary points of the Dirichlet fundamental region.
  Osaka J. Math. 16 (1979), no. 2, 439--446.
  53C21 (22E40 30F35)
• 538758
  Beem, John K.; Ehrlich, Paul E.
  Cut points, conjugate points and Lorentzian comparison theorems.
  Math. Proc. Cambridge Philos. Soc. 86 (1979), no. 2, 365--384.
  53C50 (83C99)
• 510409
  Beem, John K.; Ehrlich, Paul E.
  Singularities, incompleteness and the Lorentzian distance function.
  Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 1, 161--178.
  83D05 (58D17)
• 500702
  Ehrlich, Paul E.; Im Hof, Hans-Christoph
  Sur la géométrie des domaines de Dirichlet. (French. English summary)
  C. R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 10, A457--A458.
  53C20 (57D70)
• 493903
  Beem, John K.; Ehrlich, Paul E.
  Conformal deformations, Ricci curvature and energy conditions on globally hyperbolic spacetimes.
  Math. Proc. Cambridge Philos. Soc. 84 (1978), no. 1, 159--175.
  53C50 (83.53)
• 474137
  Ehrlich, Paul E.; Im Hof, Hans-Christoph
  Metric circles and bisectors.
  Math. Z. 159 (1978), no. 2, 101--105.
  53C25
• 523913
  Beem, John K.; Ehrlich, Paul E.
  Distance lorentzienne finie et géodésiques $f$ causales incomplètes. (French. English summary)
  C. R. Acad. Sci. Paris Sér. A-B 285 (1977), no. 16, A1129--A1131.
  83.53
• 487889
• 487888
• 487887
• 487886
• 420703
  Ehrlich, Paul Ewing
  Conformal deformations and extremal paths in the space of Riemannian metrics.
  Math. Nachr. 72 (1976), 137--140.
  58E10 (58H05 58D15)
• 397782
  Ehrlich, Paul E.
  Zwei Bemerkungen über die Ricci-Krümmung.
  Math. Z. 147 (1976), no. 1, 29--34.
  58E10 (53C20)
• 383315
  Ehrlich, Paul Ewing
  Local convex deformations of Ricci and sectional curvature on compact manifolds.
  Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Stanford Univ., Stanford, Calif., 1973), Part 1, pp. 69--71.
  Amer. Math. Soc., Providence, R.I., 1975.
  53C45
• 383293
  Ehrlich, Paul E.
  A curvature obstruction to covering deformations of connections by metric deformations.
  Proc. Amer. Math. Soc. 52 (1975), 337--342.
  53C20
• 375148
  Ehrlich, Paul E.
  Local convex deformations and sectional curvature.
  Arch. Math. (Basel) 26 (1975), no. 4, 432--435.
  53C20 (58H05)
• 417977
  Ehrlich, Paul E.
  Continuity properties of the injectivity radius function.
  Compositio Math. 29 (1974), 151--178.
  53C20 (58H05 58D15 57D70)
• 355894
  Bourguignon, Jean-Pierre; Ehrlich, Paul E.
  Champs de droites totalement géodésiques à distribution normale intégrable et courbure de Ricci. (French)
  C. R. Acad. Sci. Paris Sér. A 279 (1974), 749--752.
  53C20