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EXISTENCE OF MINIMAL HBUBBLES
, 2002
"... Given a function H ∈ C¹(R³) asymptotic to a constant at infinity, we investigate the existence of Hbubbles, i.e., nontrivial, conformal surfaces parametrized by the sphere, with mean curvature H. Under some global hypotheses we prove the existence of Hbubbles with minimal energy. ..."
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Cited by 13 (8 self)
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Given a function H ∈ C¹(R³) asymptotic to a constant at infinity, we investigate the existence of Hbubbles, i.e., nontrivial, conformal surfaces parametrized by the sphere, with mean curvature H. Under some global hypotheses we prove the existence of Hbubbles with minimal energy.
Existence of Hbubbles in a perturbative setting
 Rev. Matem. Iberoamer
"... Given a C1 function H:R3 → R, we look for Hbubbles, i.e, surfaces in R3 parametrized by the sphere S2 with mean curvature H at every regular point. Here we study the case H(u) = H0(u) + H1(u) where H0 is some “good” curvature (for which there exist H0bubbles with minimal energy, uniformly bounded ..."
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Cited by 5 (3 self)
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Given a C1 function H:R3 → R, we look for Hbubbles, i.e, surfaces in R3 parametrized by the sphere S2 with mean curvature H at every regular point. Here we study the case H(u) = H0(u) + H1(u) where H0 is some “good” curvature (for which there exist H0bubbles with minimal energy, uniformly
A note on the existence of Hbubbles via perturbation methods
, 2003
"... We study the problem of existence of surfaces in R 3 parametrized on the sphere S 2 with prescribed mean curvature H in the perturbative case, i.e. for H = H0 + εH1, where H0 is a nonzero constant, H1 is a C 2 function and ε is a small perturbation parameter. Key Words: Hsurfaces, nonlinear ellipti ..."
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Cited by 3 (0 self)
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We study the problem of existence of surfaces in R 3 parametrized on the sphere S 2 with prescribed mean curvature H in the perturbative case, i.e. for H = H0 + εH1, where H0 is a nonzero constant, H1 is a C 2 function and ε is a small perturbation parameter. Key Words: Hsurfaces, nonlinear
Hbubbles in a perturbative setting: the finitedimensional reduction method
 Duke Math. J
"... Given a regular function H: R3 → R, we look for Hbubbles, that is, regular surfaces in R3 parametrized on the sphere S2 with mean curvature H at every point. Here we study the case of H(u) = H0 + εH1(u) =: Hε(u), where H0 is a nonzero constant, ε is the smallness parameter, and H1 is any C2funct ..."
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Cited by 13 (8 self)
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Given a regular function H: R3 → R, we look for Hbubbles, that is, regular surfaces in R3 parametrized on the sphere S2 with mean curvature H at every point. Here we study the case of H(u) = H0 + εH1(u) =: Hε(u), where H0 is a nonzero constant, ε is the smallness parameter, and H1 is any C2
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of the N = 2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira– Spencer theory, which may be viewed as the closed string analog of the Chern–Simon theory. Using the mirror map this leads to computation of the ‘number ’ of holomorphic curves of higher genus curves in Calabi–Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2 theory. Relations with c = 1 strings are also pointed out.
Bayesian Interpolation
 Neural Computation
, 1991
"... Although Bayesian analysis has been in use since Laplace, the Bayesian method of modelcomparison has only recently been developed in depth. In this paper, the Bayesian approach to regularisation and modelcomparison is demonstrated by studying the inference problem of interpolating noisy data. T ..."
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Cited by 721 (17 self)
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Although Bayesian analysis has been in use since Laplace, the Bayesian method of modelcomparison has only recently been developed in depth. In this paper, the Bayesian approach to regularisation and modelcomparison is demonstrated by studying the inference problem of interpolating noisy data. The concepts and methods described are quite general and can be applied to many other problems. Regularising constants are set by examining their posterior probability distribution. Alternative regularisers (priors) and alternative basis sets are objectively compared by evaluating the evidence for them. `Occam's razor' is automatically embodied by this framework. The way in which Bayes infers the values of regularising constants and noise levels has an elegant interpretation in terms of the effective number of parameters determined by the data set. This framework is due to Gull and Skilling. 1 Data modelling and Occam's razor In science, a central task is to develop and compare models to a...
Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” Los Alamos Scientific Laboratory report
"... Several methods have been previously used to approximate free boundaries in tinitedifference numerical simulations. A simple, but powerful, method is described that is based on the concept of a fractional volume of fluid (VOF). This method is shown to be more flexible and efftcient than other method ..."
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Cited by 544 (2 self)
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Several methods have been previously used to approximate free boundaries in tinitedifference numerical simulations. A simple, but powerful, method is described that is based on the concept of a fractional volume of fluid (VOF). This method is shown to be more flexible and efftcient than other methods for treating complicated free boundary configurations. To illustrate the method, a description is given for an incompressible hydrodynamics code, SOLAVOF, that uses the VOF technique to track free fluid surfaces. 1.
Results 1  10
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