Sergiu Klainerman | Academic Influence

Sergiu Klainerman's AcademicInfluence.com Rankings

Sergiu Klainerman

Mathematics

#229

World Rank

#504

Historical Rank

#107

USA Rank

Measure Theory

#722

World Rank

#972

Historical Rank

#288

USA Rank

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Mathematics

Sergiu Klainerman's Degrees

PhD Mathematics Princeton University
Bachelors Mathematics Tel Aviv University

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Why Is Sergiu Klainerman Influential?

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According to Wikipedia, Sergiu Klainerman is a mathematician known for his contributions to the study of hyperbolic differential equations and general relativity. He is currently the Eugene Higgins Professor of Mathematics at Princeton University, where he has been teaching since 1987.

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Sergiu Klainerman's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit (1981) (865)
The Global Nonlinear Stability of the Minkowski Space. (1994) (627)
Compressible and incompressible fluids (1982) (568)
Uniform decay estimates and the lorentz invariance of the classical wave equation (1985) (496)
Space-time estimates for null forms and the local existence theorem (1993) (466)
Global existence for nonlinear wave equations (1980) (376)
Mathematical aspects of nonlinear dispersive equations (2007) (271)
Global, small amplitude solutions to nonlinear evolution equations (1983) (261)
Smoothing estimates for null forms and applications (1994) (201)
Almost global existence to nonlinear wave equations in three space dimensions (1984) (199)
On almost global existence for nonrelativistic wave equations in 3D (1996) (193)
Formation of singularities for wave equations including the nonlinear vibrating string (1980) (174)
Global existence of small amplitude solutions to nonlinear klein‐gordon equations in four space‐time dimensions (1985) (163)
Global existence of small amplitude solutions to nonlinear klein-gordon equations in four space-time dimensions (1985) (156)
Long-time behavior of solutions to nonlinear evolution equations (1982) (155)
BILINEAR ESTIMATES AND APPLICATIONS TO NONLINEAR WAVE EQUATIONS (2001) (153)
Decay and regularity for the schrödinger equation (1992) (150)
On the Maxwell-Klein-Gordon equation with finite energy (1994) (148)
On the Uniqueness of Solutions to the Gross-Pitaevskii Hierarchy (2007) (147)
Remarks on the global sobolev inequalities in the minkowski space Rn+1 (1987) (141)
Remark on the optimal regularity for equations of wave maps type (1997) (135)
Bilinear space-time estimates for homogeneous wave equations (2000) (134)
Asymptotic properties of linear field equations in minkowski space (1990) (125)
The Bounded L2 Curvature Conjecture (2012) (110)
The Evolution Problem in General Relativity (2002) (108)
Finite energy solutions of the Yang-Mills equations in $\mathbb{R}^{3+1}$ (1995) (105)
On the optimal local regularity for the Yang-Mills equations in ℝ⁴⁺¹ (1999) (96)
A new approach to study the Vlasov-Maxwell system (2001) (94)
Rough solutions of the Einstein vacuum equations (2001) (90)
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations (2017) (88)
Improved local well-posedness for quasilinear wave equations in dimension three (2003) (87)
On the optimal local regularity for Yang-Mills equations in R 4 + 1 (2007) (85)
On the uniqueness of smooth, stationary black holes in vacuum (2007) (81)
Shock Formation in Small-Data Solutions to $3D$ Quasilinear Wave Equations: An Overview (2014) (80)
On the global regularity of wave maps in the critical Sobolev norm (2000) (79)
Remark on Strichartz-Type Inequalities (1996) (76)
Uniqueness of Smooth Stationary Black Holes in Vacuum: Small Perturbations of the Kerr Spaces (2009) (76)
ON LOCAL AND GLOBAL ASPECTS OF THE CAUCHY PROBLEM IN GENERAL RELATIVITY (1999) (74)
Causal geometry of Einstein-Vacuum spacetimes with finite curvature flux (2003) (72)
On the regularity properties of a model problem related to wave maps (1997) (71)
A geometric approach to the Littlewood–Paley theory (2003) (60)
The bounded $$L^2$$L2 curvature conjecture (2015) (58)
Rough solutions of the Einstein-vacuum equations (2005) (46)
A commuting vectorfields approach to Strichartz-type inequalities and applications to quasi-linear wave equations (2000) (46)
Hawking’s Local Rigidity Theorem Without Analyticity (2009) (45)
On “almost global” solutions to quasilinear wave equations in three space dimensions (1983) (44)
On the breakdown criterion in general relativity (2008) (44)
CORRIGENDUM: Peeling properties of asymptotically flat solutions to the Einstein vacuum equations (2004) (43)
On the optimal local regularity for gauge field theories (1997) (42)
A fully anisotropic mechanism for formation of trapped surfaces in vacuum (2013) (41)
Remark on the asymptotic behavior of the klein gordon equation in ℝn+1 (1993) (41)
PDE as a Unified Subject (2010) (41)
Weighted L∞ and L1 estimates for solutions to the classical wave equation in three space dimensions (1984) (39)
Uniqueness Results for Ill-Posed Characteristic Problems in Curved Space-Times (2007) (37)
Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux (2003) (35)
ON THE RADIUS OF INJECTIVITY OF NULL HYPERSURFACES. (2006) (34)
On the Regularity of Classical Field Theories in Minkowski Space-Time R3+1 (1997) (31)
On the local extension of Killing vector-fields in Ricci flat manifolds (2011) (30)
A KIRCHOFF–SOBOLEV PARAMETRIX FOR THE WAVE EQUATION AND APPLICATIONS (2006) (28)
Rigidity of stationary black holes with small angular momentum on the horizon (2013) (28)
Overview of the proof of the Bounded L 2 Curvature Conjecture (2012) (27)
On emerging scarred surfaces for the Einstein vacuum equations (2010) (27)
The causal structure of microlocalized rough Einstein metrics (2005) (26)
RICCI DEFECTS OF MICROLOCALIZED EINSTEIN METRICS (2001) (22)
A physical space approach to wave equation bilinear estimates (2001) (22)
BILINEAR ESTIMATES ON CURVED SPACE–TIMES (2005) (21)
On the algebraic properties of the Hn/2, 1/2 spaces (1998) (19)
On the Regularity Properties of the Wave Equation (1994) (15)
On Nash’s unique contribution to analysis in just three of his papers (2016) (15)
Kerr stability for small angular momentum (2021) (15)
Noncompact problems at the intersection of geometry, analysis, and topology : proceedings of the Brezis-Browder Conference, Noncompact Variational Problems and General Relativity, October 14-18, 2001, Rutgers, the State University of New Jersey, New Brunswick, NJ (2004) (14)
Mathematical challenges of General Relativity (2007) (14)
Rigidity Results in General Relativity: a Review (2015) (14)
Explicit solutions of $\square u = 0$ on the Friedmann-Robertson-Walker space-times (1981) (11)
On the work and legacy of Fritz John, 1934-1991 (1998) (10)
A general formalism for the stability of Kerr (2020) (10)
Rough solution for the Einstein Vacuum equations (2001) (9)
Construction of GCM Spheres in Perturbations of Kerr (2019) (9)
On the mathematical theory of classical fields and general relativity (1992) (8)
Effective Results on Uniformization and Intrinsic GCM Spheres in Perturbations of Kerr (2019) (7)
The causal structure of microlocalized Einstein metrics (2001) (6)
The Error Estimates (2003) (6)
The nonlinear stability of the Minkowski metric in general relativity (1989) (6)
Wave equations estimates and the nonlinear stability of slowly rotating Kerr black holes (2022) (5)
Einstein Geometry and Hyperbolic Equations (1987) (5)
The resolution of the bounded L2 curvature conjecture in general relativity (2016) (4)
Sharp L1 estimates for singular transport equations (2007) (4)
Regularity and geometric properties of solutions of the Einstein-Vacuum equations (2002) (3)
A fully anisotropic mechanism for formation of trapped surfaces in vacuum (2014) (2)
Mathematical Aspects of Nonlinear Dispersive Equations (AM-163) (2009) (2)
Is the Fields Medal the Nobel Prize of Mathematics (2015) (1)
On the regularity properties of non-linear wave equations (1997) (1)
RECENT RESULTS IN MATHEMATICAL GR (2013) (1)
COSMIC CENSORSHIP AND OTHER GREAT MATHEMATICAL CHALLENGES OF GENERAL RELATIVITY (2009) (1)
Brief introduction to the nonlinear stability of Kerr (2022) (1)
The resolution of the bounded L2 curvature conjecture in general relativity (2016) (1)
IV.12 Partial Differential Equations (2010) (1)
On bilinear estimates for wave equations (1999) (1)
CHAPTER 2. Generalized Hodge Systems in 2-D (1994) (0)
General Relativity and the Einstein Equations (2010) (0)
Initialization and Extension (Theorems M6, M7, M8) (2020) (0)
Estimates for the Connection Coefficients (2003) (0)
Definitions and Results (2003) (0)
Chapter Ten. On the Bounded L2 Curvature Conjecture (2014) (0)
Gafa Geometric and Functional Analysis Pde as a Unified Subject (2003) (0)
Linear and nonlinear field equations (1987) (0)
Decay Estimates for q (Theorem M1) (2020) (0)
Consequences of the Bootstrap Assumptions (2020) (0)
The Initial Hypersurface and the Last Slice (2003) (0)
CHAPTER 8. The Error Estimates (1994) (0)
On the algebraic properties of the $H_{\frac{n}{2},{\frac{1}{2}}}$ spaces (1998) (0)
The Unity of Partial Differential Equations (2020) (0)
CHAPTER 15. The Matching (1994) (0)
Louis Nirenberg (1925–2020) (2021) (0)
The bounded L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document} curvature conjecture (2015) (0)
Decay Estimates (Theorems M4, M5) (2020) (0)
HAWKING ’ S LOCAL RIGIDITY THEOREM WITHOUT (2009) (0)
CHAPTER 14. The Last Slice (1994) (0)
CHAPTER 16. The Rotation Vectorfields (1994) (0)
Estimates for the Riemann Curvature Tensor (2003) (0)
CHAPTER 9. Construction of the Optical Function (1994) (0)
Reflections on an Essay by Wigner (2022) (0)
Analytic Methods in the Study of the Initial Value Problem (2003) (0)
Stability of Minkowski Space (2004) (0)
CHAPTER 11. Second Fundamental Form (1994) (0)
Around the bounded $L^2$ curvature conjecture in general relativity (2008) (0)
Decay Estimates for α‎ and α‎ (Theorems M2, M3) (2020) (0)
Existence of finitely perturbed Friedmann models via the Cauchy problem (2017) (0)
Partial differential equations (2003) (0)
Commentary on [77], [85], [92], and [94] (1985) (0)
On the algebraic properties of the Hn2,12 spaces (2008) (0)
CHAPTER 10. Third Version of the Main Theorem (1994) (0)
Main Theorem (2020) (0)
CHAPTER 17. Conclusions (1994) (0)
0 n the mathematical theory of classical fi elds and general relativity (2017) (0)
On the dynamic formation of trapped surfaces in vacuum (2013) (0)
CHAPTER 6. Deformation of 2-Surfaces in 3-D (1994) (0)
On bilinear restriction type estimates and applications to nonlinear wave equations (1998) (0)
GCM Procedure (2020) (0)
CHAPTER 5. Curvature of an Initial Data Set (1994) (0)
Introduction (2020) (0)
On the Global Stability of the Wave-map Equation in Kerr Spaces with Small Angular Momentum (2015) (0)
CHAPTER 13. Derivatives of the Optical Function (1994) (0)
Regge-Wheeler Type Equations (2020) (0)
CHAPTER 3. General Results in 3-D Geometry (1994) (0)
Macarthur fellowships given for physics-related work (1991) (0)
Preliminaries (2020) (0)
CHAPTER 12. The Lapse Function (1994) (0)
CHAPTER 4. The Poisson Equation in 3-D (1994) (0)
CHAPTER 7. The Comparison Theorem (1994) (0)

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