Paul M. Feehan
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(Suggest an Edit or Addition)According to Wikipedia, Paul Matthew Niall Feehan studied electrical engineering at University College Dublin and the University of Missouri at Rolla , before switching to mathematics. His 1992 Ph.D. on "Geometry of the Moduli Space of Self-Dual Connections on the Four-Sphere" was done at Columbia University under Duong Hong Phong.
Paul M. Feehan'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
- $\rm PU(2)$ monopoles. I. Regularity, Uhlenbeck compactness, and transversality (1997) (62)
- Global existence and convergence of solutions to gradient systems and applications to Yang-Mills gradient flow (2014) (40)
- A SCHAUDER APPROACH TO DEGENERATE-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED COEFFICIENTS (2011) (32)
- Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations (2012) (31)
- PU(2) monopoles and relations between four-manifold invariants (1997) (31)
- Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations (2012) (26)
- PU(2) MONOPOLES. II: TOP-LEVEL SEIBERG-WITTEN MODULI SPACES AND WITTEN'S CONJECTURE IN LOW DEGREES (1997) (23)
- C^{1,1} regularity for degenerate elliptic obstacle problems (2012) (23)
- Generic metrics, irreducible rank-one PU(2) monopoles, and transversality (1998) (23)
- Geometry of the ends of the moduli space of anti-self-dual connections (2015) (22)
- PU(2) monopoles and links of top-level Seiberg-Witten moduli spaces. (2000) (22)
- SO(3) monopoles, level-one Seiberg–Witten moduli spaces, and Witten's conjecture in low degrees (2001) (22)
- PU(2) monopoles. III: Existence of gluing and obstruction maps (1999) (21)
- Maximum Principles for Boundary-Degenerate Second Order Linear Elliptic Differential Operators (2012) (21)
- Existence, uniqueness, and global regularity for degenerate elliptic obstacle problems in mathematical finance (2011) (20)
- Energy gap for Yang–Mills connections, II: Arbitrary closed Riemannian manifolds ☆ (2015) (19)
- Stochastic representation of solutions to degenerate elliptic and parabolic boundary value and obstacle problems with Dirichlet boundary conditions (2012) (19)
- Łojasiewicz–Simon gradient inequalities for analytic and Morse–Bott functions on Banach spaces (2015) (19)
- Degenerate elliptic operators in mathematical finance and Holder continuity for solutions to variational equations and inequalities (2011) (19)
- Global existence and convergence of smooth solutions to Yang-Mills gradient flow over compact four-manifolds (2014) (19)
- Donaldson invariants and wall-crossing formulas. I: Continuity of gluing maps (1998) (18)
- PU(2) monopoles, II: Highest-level singularities and relations between four-manifold invariants (1997) (17)
- On the martingale problem for degenerate-parabolic partial differential operators with unbounded coefficients and a mimicking theorem for Ito processes (2012) (17)
- Lojasiewicz-Simon gradient inequalities for analytic and Morse-Bott functionals on Banach spaces and applications to harmonic maps (2015) (17)
- {\boldmath{$\operatorname{PU}(2)$} monopoles and a conjecture of Mariño, Moore, and Peradze (1998) (17)
- Boundary-degenerate elliptic operators and Holder continuity for solutions to variational equations and inequalities (2011) (16)
- On Donaldson and Seiberg-Witten invariants (2001) (15)
- Energy gap for Yang–Mills connections, I: Four-dimensional closed Riemannian manifolds (2014) (15)
- PARTIAL DIFFERENTIAL OPERATORS WITH NON-NEGATIVE CHARACTERISTIC FORM, MAXIMUM PRINCIPLES, AND UNIQUENESS FOR BOUNDARY VALUE AND OBSTACLE PROBLEMS (2013) (15)
- Witten's Conjecture for many four-manifolds of simple type (2006) (15)
- Critical-exponent Sobolev norms and the Slice Theorem for the quotient space of connections (1997) (14)
- Degenerate-parabolic partial differential equations with unbounded coefficients, martingale problems, and a mimicking theorem for Ito processes (2011) (13)
- An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg–Witten Invariants (2002) (12)
- A classical Perron method for existence of smooth solutions to boundary value and obstacle problems for degenerate-elliptic operators via holomorphic maps (2013) (12)
- Superconformal simple type and Witten's conjecture (2014) (11)
- Resolution of singularities and geometric proofs of the Łojasiewicz inequalities (2017) (11)
- On the Morse–Bott property of analytic functions on Banach spaces with Łojasiewicz exponent one half (2018) (11)
- The SO(3) monopole cobordism and superconformal simple type (2014) (10)
- LOJASIEWICZ – SIMON GRADIENT INEQUALITIES FOR ANALYTIC AND MORSE – BOTT FUNCTIONS ON BANACH SPACES (2019) (9)
- Optimal Łojasiewicz–Simon inequalities and Morse–Bott Yang–Mills energy functions (2017) (7)
- Łojasiewicz–Simon gradient inequalities for coupled Yang–Mills energy functions (2015) (7)
- A Kato-Yau inequality and decay estimate for eigenspinors (1999) (6)
- Maximum principles for boundary-degenerate linear elliptic differential operators (2012) (6)
- Maximum principles for boundary-degenerate linear parabolic differential operators (2013) (5)
- SO(3)-MONOPOLES: THE OVERLAP PROBLEM (2012) (4)
- Discreteness for energies of Yang-Mills connections over four-dimensional manifolds (2015) (4)
- Morse theory for the Yang-Mills energy function near flat connections (2019) (4)
- Analysis, complex geometry, and mathematical physics : in honor of Duong H. Phong : May 7-11, 2013, Columbia University, New York, New York (2015) (4)
- Relative energy gap for harmonic maps of Riemann surfaces into real analytic Riemannian manifolds (2016) (4)
- Feynman-Kac Formulas for Solutions to Degenerate Elliptic and Parabolic Boundary-Value and Obstacle Problems with Dirichlet Boundary Conditions (2015) (3)
- A Kato-Yau inequality and decay estimate for harmonic spinors (1999) (3)
- Geometry of the Moduli Space of Self-Dual Connections Over the Four-Sphere (1992) (3)
- Perturbations of local maxima and comparison principles for boundary-degenerate linear differential equations (2013) (2)
- UHLENBECK COMPACTNESS AND TRANSVERSALITY FOR THE MODULI SPACE OF PU(2) MONOPOLES 1 (1997) (2)
- Homotopy equivalence and Donaldson invariants when b^+ = 1. I: Cobordisms of moduli spaces and continuity of gluing maps (1998) (1)
- Gluing in geometric analysis via maps of Banach manifolds with corners and applications to gauge theory. (2019) (1)
- Virtual Morse-Bott index, moduli spaces of pairs, and applications to topology of smooth four-manifolds (2020) (1)
- Lojasiewicz--Simon gradient inequalities for the harmonic map energy function (2019) (1)
- Introduction to virtual Morse-Bott theory, moduli spaces of SO(3) monopoles, and applications to four-manifolds (2020) (0)
- Ja n 20 15 ENERGY GAP FOR YANG-MILLS CONNECTIONS OVER FOUR-DIMENSIONAL CLOSED RIEMANNIAN MANIFOLDS (2022) (0)
- LINKS OF LEVEL ONE REDUCIBLE PU ( 2 ) (1999) (0)
- An investigation of methods of surface estimation with application to the interpolation of antenna patterns (1984) (0)
- An $L^2$ energy gap for Yang-Mills connections over four-dimensional Riemannian manifolds (2014) (0)
- Researching Rock n' Roll: A Guide to Reference Sources (1987) (0)
- SHORT READING COURSE ON YANG–MILLS GAUGE THEORY AND APPLICATIONS TO LOW-DIMENSIONAL TOPOLOGY (2019) (0)
- Lojasiewicz–Simon gradient inequality on a Sobolev neighborhood of a flat connection (2017) (0)
- PRIORI ESTIMATES AND REGULARITY OF SOLUTIONS TO BOUNDARY-DEGENERATE ELLIPTIC LINEAR SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS (2013) (0)
- Introduction to virtual Morse-Bott theory on analytic spaces, moduli spaces of SO(3) monopoles, and applications to four-manifolds. (2020) (0)
- On the Morse–Bott property of analytic functions on Banach spaces with Łojasiewicz exponent one half (2020) (0)
- Bialynicki-Birula theory, Morse-Bott theory, and resolution of singularities for analytic spaces (2022) (0)
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