Jim Isenberg

James A. Isenberg works on partial differential equations and geometric analysis, with an emphasis on general relativity and geometric heat flows. He is currently focusing on the study of solutions of the Einstein constraint equations, on strong cosmic censorship and the nature of singularities in general relativistic models of the universe, and on the formation of singularities in Ricci flow and mean curvature flow. The author of over 120 papers and 5 books, he has held visiting positions at Oxford, Paris, Potsdam, Stockholm, Vienna, and Canberra, as well as at several places in this country.

Research Interests

1. Mathematical Relativity
   
   • Solutions of the Einstein constraint equations
   • The nature of cosmological solutions in the neighborhood of the big bang
   • Cosmic censorship
2. Geometric Heat Flow
   
   • Ricci flow of geometries with symmetry
   • Stability of converging and of collapsing Ricci flows
   • Asymptotic behavior of neckpinches in Ricci flow and mean curvature flow
   • Solutions of the RG-2 (Renormalization Group) Flow
3. Nonlinear Wave Equations
   
   • Critical behavior in wave maps
   • Singularities in Lorentz wave maps
   • Long time behavior of timelike minimal submanifolds
4. Momentum maps and classical field theory
   

Papers

• Sectoriality of the Laplacian on Asymptotically Hyperbolic Spaces
  with Eric Bahuaud and Christine Guenther.
• Stability of Asymptotic Behavior Within Polarised T2-Symmetric Vacuum Solutions with Cosmological Constant
  with Ellery Ames, Florian Beyer and Todd Oliynyk. Phil. Trans. R. Soc. A. 380: 20210173.
• A Phase Space Approach to the Conformal Construction of Non-Vacuum Initial Data Sets in General Relativity
  with David Maxwell.
• A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with Type-II curvature blowup
  with David Garfinkle, Dan Knopf, and Haotian Wu. Nonlinearity 34 (2021), no. 9, 6539--6560.
• Stability of AVTD Behavior within the Polarized T2-symmetric vacuum spacetimes
  with Ellery Ames, Florian Beyer, and Todd Oliynyk. Ann. Henri Poincaré (2022).
• Singularity formation of complete Ricci flow solutions
  with Timothy Carson, Dan Knopf, and Natasa Sesum.
• On the precise asymptotics of Type-IIb solutions to mean curvature flow
  with Haotian Wu and Zhou Zhang.
• Asymptotic gluing of shear-free hyperboloidal initial data sets
  with Paul T. Allen, John M. Lee, and Iva Stavrov Allen. Ann. Henri Poincaré 22 (2021), no. 3, 771--819.
• Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up. II
  with Haotian Wu and Zhou Zhang. Adv. Math. 367 (2020), 107111, 44 pp.
• Contracting asymptotics of the lapse-scalar field sub-system of the Einstein-scalar field equations
  with Ellery Ames and Florian Beyer. J. Math. Phys. 60 (2019), 102504.
• Stability Within T2-Symmetric Expanding Spacetimes
  with Beverly K. Berger and Adam Layne. Annales Henri Poincaré, Vol. 21, pp. 675--703 (2020)
• Symmetries of Cosmological Cauchy Horizons with Non-Closed Orbits
  with Vincent Moncrief. Comm. Math. Phys.
• Convergence Stability for Ricci Flow
  with Eric Bahuaud and Christine Guenther. J. Geom. Anal., Vol. 30, pp. 31--336 (2020)
• Non-Kahler Ricci flow singularities that converge to Kahler-Ricci solitons
  with Dan Knopf and Natasa Sesum. Pure Appl. Math. Q. 15 (2019), no. 2, pp. 749-784.
• General Relativity, Time and Determinism
  an invited and refereed contribution to Space Time and the Limits of Human Understanding
• Existence and Blowup Results for Asymptotically Euclidean Initial Data Sets Generated by the Conformal Method
  with James Dilts. Phys. Rev. D 94 (2016), no. 10, 104046, 14 pp.
• Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up
  with Haotian Wu. J. Reine Angew. Math.
• A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges
  with Ellery Ames, Florian Beyer and Philippe G. LeFloch. J. Geom. Phys. 121 (2017), 42--71.
• The shear-free condition and constant-mean-curvature hyperboloidal initial data
  with Paul T. Allen, John M. Lee and Iva Stavrov Allen. Classical Quantum Gravity 33 (2016), no. 11.
• Weakly asymptotically hyperbolic manifolds
  with Paul T. Allen, John M. Lee and Iva Stavrov Allen. Comm. Anal. Geom. 26 (2018), no. 1, 1–61.
• On Strong Cosmic Censorship
  Surv. Differ. Geom., 20, 17–36.
• General Relativity and Gravitation: A Centennial Perspective
  with Abhay Ashtekar, Beverly Berger, and Malcolm A. H. MacCallum. For the full volume, see Cambridge University Press.
• Short-time existence for the second order renormalization group flow in general dimensions
  with Karsten Gimre and Christine Guenther. Proc. Amer. Math. Soc. 143 (2015), no. 10, 4397–4401.
• A geometric introduction to the two-loop renormalization group flow
  with Karsten Gimre and Christine Guenther. J. Fixed Point Theory Appl. 14 (2013), no. 1, 3–20.
• Ricci flow neckpinches without rotational symmetry
  with Dan Knopf and Natasa Sesum. Comm. Partial Differential Equations 41 (2016), no. 12, 1860–1894.
• Non-CMC solutions of the Einstein constraint equations on asymptotically Euclidean manifolds
  with James Dilts, Rafe Mazzeo, and Caleb Meier. Classical Quantum Gravity 31 (2014), no. 6, 065001, 10 pp.
• Power law inflation with electromagnetism
  with Xianghui Luo. Ann. Physics 334 (2013), 420–454.
• Degenerate neckpinches in Ricci flow
  with Sigurd Angenent and Dan Knopf.
• On the constraint equations in Einstein-aether theories and the weak gravitational field limit
  with David Garfinkle and Jose M. Martin-Garcia. Phys. Rev. D 86, 084009.
• Quasilinear symmetric hyperbolic Fuchsian systems in several space dimensions
  with Ellery Ames, Florian Beyer, and Philippe LeFloch. Complex analysis and dynamical systems V, 25–43, Contemp. Math., 591, 2013.
• Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimes
  with Ellery Ames, Florian Beyer, and Philippe LeFloch. Ann. Henri Poincaré 14 (2013), no. 6, 1445–1523.
• Second-order renormalization group flow of three-dimensional homogeneous geometries
  with Karsten Gimre and Christine Guenther. Comm. Anal. Geom. 21 (2013), no. 2, 435–467.
• Ricci flow on asymptotically conical surfaces with nontrivial topology
  with Rafe Mazzeo and Natasa Sesum. J. Reine Angew. Math. 676 (2013), 227–248.
• Ricci flow in two dimensions
  with Rafe Mazzeo and Natasa Sesum. Surveys in geometric analysis and relativity, 259–280, Adv. Lect. Math. (ALM), 20, 2011.
• Asymptotic gluing of asymptotically hyperbolic vacuum initial data sets
  with John Lee and Iva Stavrov Allen. Complex analysis and dynamical systems IV. Part 2, 93–103, Contemp. Math., 554, 2011.
• Construction of N-body time-symmetric initial data sets in general relativity
  with Piotr Chruściel and Justin Corvino. Complex analysis and dynamical systems IV. Part 2, 83–92, Contemp. Math., 554, 2011.
• Formal matched asymptotics for degenerate Ricci flow neckpinches
  with Sigurd Angenent and Dan Knopf. Nonlinearity 24 (2011), no. 8, 2265–2280.
• Construction of N-body initial data sets in general relativity
  with Piotr Chruściel and Justin Corvino. Comm. Math. Phys. 304 (2011), no. 3, 637–647.
• Asymptotic gluing of asymptotically hyperbolic solutions to the Einstein constraint equations
  with John Lee and Iva Stavrov Allen. Ann. Henri Poincaré 11 (2010), no. 5, 881–927.
• Initial data for the relativistic gravitational N-body problem
  with Piotr Chruściel and Justin Corvino. Classical Quantum Gravity 27 (2010), no. 22, 222002, 6 pp.
• Convergence of Ricci flow on R2 to flat space
  with Mohammad Javaheri. J. Geom. Anal. 19 (2009), no. 4, 809–816.
• Symmetries of higher dimensional black holes
  with Vincent Moncrief. Classical Quantum Gravity 25 (2008), no. 19, 195015, 37 pp.
• The modeling of degenerate neck pinch singularities in Ricci flow by Bryant solitons
  with David Garfinkle. J. Math. Phys. 49 (2008), no. 7, 073505, 10 pp.
• Waveless approximation theories of gravity
  Internat. J. Modern Phys. D 17 (2008), no. 2, 265–273.
• Near-constant mean curvature solutions of the Einstein constraint equations with non-negative
  with Adam Clausen and Paul T Allen. Classical Quantum Gravity 25 (2008), no. 7, 075009, 15 pp.
• Areal foliation and asymptotically velocity-term dominated behavior in T2 symmetric space-times with positive cosmological constant
  with Adam Clausen. J. Math. Phys. 48 (2007), no. 8, 082501, 17 pp.
• The Ricci flow: techniques and applications
  with Ben Chow, Sun-Chin Chu, David Glickenstein, Christine Guenther, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, and Lei Ni. Part I Part II Part III Part IV
• The constraint equations for the Einstein-scalar field system on compact manifolds
  with Yvonne Choquet-Bruhat and Daniel Pollack. Classical Quantum Gravity 24 (2007), no. 4, 809–828.
• Applications of theorems of Jean Leray to the Einstein-scalar field equations
  with Yvonne Choquet-Bruhat and Daniel Pollack. J. Fixed Point Theory Appl. 1 (2007), no. 1, 31–46.
• Timelike minimal submanifolds of general co-dimension in Minkowski space time
  with Paul Allen and Lars Andersson. J. Hyperbolic Differ. Equ. 3 (2006), no. 4, 691–700.
• Linear stability of homogeneous Ricci solitons
  with Christine Guenther and Dan Knopf. Int. Math. Res. Not. 2006.
• Ricci flow on locally homogeneous closed 4-manifolds
  with Martin Jackson and Peng Lu. Comm. Anal. Geom. 14 (2006), no. 2, 345–386.
• Half polarized U(1) symmetric vacuum spacetimes with AVTD behavior
  with Yvonne Choquet-Bruhat. J. Geom. Phys. 56 (2006), no. 8, 1199–1214.
• Spherically symmetric dynamical horizons
  with Robert Bartnik. Classical Quantum Gravity 23 (2006), no. 7, 2559–2569.
• The Einstein-scalar field constraints on asymptotically Euclidean manifolds
  with Yvonne Choquet-Bruhat and Daniel Pollack. Chinese Ann. Math. Ser. B 27 (2006), no. 1, 31–52.
• A gluing construction for non-vacuum solutions of the Einstein-constraint equations
  with David Maxwell and Daniel Pollack. Adv. Theor. Math. Phys. 9 (2005), no. 1, 129–172.
• Initial data engineering
  with Piotr Chrusciel and Daniel Pollack. Comm. Math. Phys. 257 (2005), no. 1, 29–42.
• Numerical studies of the behavior of Ricci flow
  with David Garfinkle. Geometric evolution equations, 103–114, Amer. Math. Soc.
• Topologically general U(1) symmetric vacuum space-times with AVTD behavior
  with Yvonne Choquet-Bruhat and Vince Moncrief. Nuovo Cimento Soc. Ital. Fis. B 119 (2004), no. 7-9, 625–638.
• The Constraint Equations
  with Robert Bartnik. The Einstein equations and the large scale behavior of gravitational fields, 1–38, Birkhäuser, Basel, 2004.
• Gluing initial data sets for general relativity
  with Piotr Chrusciel and Daniel Pollack. Phys. Rev. Lett. 93, 081101.
• Critical Behavior in Ricci Flow
  with David Garfinkle
• Non CMC Conformal Data Sets Which Do Not Produce Solutions of the Einstein Constraint Equations
  with Niall Ó Murchadha. Class. Quant. Grav. 21 (2004) S233-S242.
• On the area of the symmetry orbits in T2 symmetric spacetimes
  with Marsha Weaver. Classical Quantum Gravity 20 (2003), no. 16, 3783–3796.
• On the topology of vacuum spacetimes
  with Rafe Mazzeo and Daniel Pollack. Ann. Henri Poincaré 4 (2003), no. 2, 369–383.
• Constructing solutions of the Einstein constraint equations
  General relativity & gravitation (Durban, 2001), 174–191, World Sci. Publ., 2002.
• Gluing and wormholes for the Einstein constraint equations
  with Rafe Mazzeo and Daniel Pollack. Comm. Math. Phys. 231 (2002), no. 3, 529–568.
• Asymptotic behaviour in polarized and half-polarized U(1) symmetric vacuum spacetimes
  with Vince Moncrief. Classical Quantum Gravity 19 (2002), no. 21, 5361–5386.
• Stability of the Ricci flow at Ricci-flat metrics
  with Christine Guenther and Dan Knopf. Comm. Anal. Geom. 10 (2002), no. 4, 741–777.
• Singularity formation in 2+1 wave maps
  with Steven L. Liebling. J. Math. Phys. 43 (2002), no. 1, 678–683.
• Oscillatory approach to the singularity in vacuum spacetimes with T2 isometry
  with Beverly Berger and Marsha Weaver. Phys. Rev. D (3) 64 (2001), no. 8, 084006, 20 pp. Phys. Rev. D 67, 129901.
• Einstein constraints on asymptotically Euclidean manifolds
  with Yvonne Choquet-Bruhat and James W. York, Jr. Phys. Rev. D (3) 61 (2000), no. 8, 084034, 20 pp.
• Existence, uniqueness and other properties of the BCT (minimal strain lapse and shift) gauge
  with David Garfinkle, Carsten Gundlach, and Niall Ó Murchadha. Classical Quantum Gravity 17 (2000), no. 18, 3899–3904.
• Global existence for wave maps with torsion
  with Stephen C. Anco. Comm. Partial Differential Equations 25 (2000), no. 9-10, 1669--1702.
• Critical phenomena in nonlinear sigma models
  with Steven L. Liebling and Eric W. Hirschmann. J. Math. Phys. 41 (2000), no. 8, 5691--5700.
For older papers, see CV.