Free Access
Issue |
ESAIM: M2AN
Volume 46, Number 1, January-February 2012
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Page(s) | 59 - 79 | |
DOI | https://doi.org/10.1051/m2an/2011019 | |
Published online | 22 July 2011 |
- F. Almgren and J.E. Taylor, Optimal geometry in equilibrium and growth. Fractals 3 (1995) 713–723. Symposium in Honor of B. Mandelbrot. [CrossRef] [MathSciNet] [Google Scholar]
- F. Almgren, J.E. Taylor and L. Wang, Curvature-driven flows: a variational approach. SIAM J. Control Optim. 31 (1993) 387–438. [Google Scholar]
- L. Ambrosio, Minimizing movements. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. 19 (1995) 191–246. [MathSciNet] [Google Scholar]
- L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures. Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel (2005). [Google Scholar]
- J.W. Barrett, H. Garcke and R. Nürnberg, Parametric approximation of Willmore flow and related geometric evolution equations. SIAM J. Sci. Comput. 31 (2008) 225–253. [CrossRef] [MathSciNet] [Google Scholar]
- M. Bauer and E. Kuwert, Existence of minimizing Willmore surfaces of prescribed genus. Int. Math. Res. Not. 10 (2003) 553–576. [CrossRef] [Google Scholar]
- T. Baumgart, S.T. Hess and W.W. Webb, Image coexisting fluid domains in biomembrane models coupling curvature and line tension. Nature 425 (2003) 821–824. [CrossRef] [PubMed] [Google Scholar]
- G. Bellettini and M. Paolini, Anisotropic motion by mean curvature in the context of Finsler geometry. Hokkaido Math. J. 25 (1996) 537–566. [MathSciNet] [Google Scholar]
- A. Bonito, R.H. Nochetto and M.S. Pauletti, Parametric FEM for geometric biomembranes. J. Comput. Phys. 229 (2010) 3171–3188. [CrossRef] [MathSciNet] [Google Scholar]
- J.W. Cahn and D.W. Hoffman, A vector thermodynamics for anisotropic surfaces. II. Curved and facetted surfaces. Acta Metall. 22 (1974) 1205–1214. [CrossRef] [Google Scholar]
- T. Chan and L. Vese, A level set algorithm for minimizing the Mumford-Shah functional in image processing, in Proceedings of the 1st IEEE Workshop on Variational and Level Set Methods in Computer Vision (2001) 161–168. [Google Scholar]
- K. Chen, C. Jayaprakash, R. Pandit and W. Wenzel, Microemulsions: A Landau-Ginzburg theory. Phys. Rev. Lett. 65 (1990) 2736–2739. [CrossRef] [PubMed] [Google Scholar]
- P. Cicuta, S.L. Keller and S.L. Veatch, Diffusion of liquid domains in lipid bilayer membranes. J. Phys. Chem. B 111 (2007) 3328–3331. [CrossRef] [PubMed] [Google Scholar]
- U. Clarenz, U. Diewald, G. Dziuk, M. Rumpf and R. Rusu, A finite element method for surface restoration with smooth boundary conditions. Comput. Aided Geom. Des. 21 (2004) 427–445. [Google Scholar]
- M.C. Delfour and J.-P. Zolésio, Shapes and Geometries, Advances in Design and Control. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2001). [Google Scholar]
- H.G. Döbereiner, O. Selchow and R. Lipowsky, Spontaneous curvature of fluid vesicles induced by trans-bilayer sugar asymmetry. Eur. Biophys. J. 28 (1999) 174–178. [CrossRef] [Google Scholar]
- G. Doğan, P. Morin and R.H. Nochetto, A variational shape optimization approach for image segmentation with a Mumford-Shah functional. SIAM J. Sci. Comput. 30 (2008) 3028–3049. [CrossRef] [MathSciNet] [Google Scholar]
- G. Doğan, P. Morin, R.H. Nochetto and M. Verani, Discrete gradient flows for shape optimization and applications. Comput. Meth. Appl. Mech. Eng. 196 (2007) 3898–3914. [Google Scholar]
- M. Droske and M. Bertozzi, Higher-order feature-preserving geometric regularization. SIAM J. Imaging Sci. 3 (2010) 21–51. [CrossRef] [MathSciNet] [Google Scholar]
- G. Dziuk, Computational parametric Willmore flow. Numer. Math. 111 (2008) 55–80. [CrossRef] [MathSciNet] [Google Scholar]
-
G. Dziuk, E. Kuwert and R. Schätzle, Evolution of elastic curves in
: existence and computation. SIAM J. Math. Anal. 33 (electronic) (2002) 1228–1245. [Google Scholar]
- C.M. Elliott and B. Stinner, Modeling and computation of two phase geometric biomembranes using surface finite elements. J. Comput. Phys. 229 (2010) 6585–6612. [CrossRef] [MathSciNet] [Google Scholar]
- W. Helfrich, Elastic properties of lipid bilayers – theory and possible experiments. Zeitschrift Fur Naturforschung C-A J. Biosc. 28 (1973) 693. [Google Scholar]
- M. Hintermüller and W. Ring, A second order shape optimization approach for image segmentation. SIAM J. Appl. Math. 64 (2003/04) 442–467. [Google Scholar]
- M. Hintermüller and W. Ring, An inexact Newton-CG-type active contour approach for the minimization of the Mumford-Shah functional. J. Math. Imaging and Vision 20 (2004) 19–42. Special issue on mathematics and image analysis. [Google Scholar]
- J.T. Jenkins, The equations of mechanical equilibrium of a model membrane. SIAM J. Appl. Math. 32 (1977) 755–764. [CrossRef] [MathSciNet] [Google Scholar]
- R. Keriven and O. Faugeras, Variational principles, surface evolution, PDEs, level set methods and the stereo problem. Technical Report 3021, INRIA (1996). [Google Scholar]
- R. Keriven and O. Faugeras, Variational principles, surface evolution, PDEs, level set methods and the stereo problem. IEEE Trans. Image Process. 7 (1998) 336–344. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- R. Kimmel and A.M. Bruckstein, Regularized Laplacian zero crossings as optimal edge integrators. IJCV 53 (2003) 225–243. [CrossRef] [Google Scholar]
- E. Kuwert and R. Schätzle, The Willmore flow with small initial energy. J. Differential Geom. 57 (2001) 409–441. [MathSciNet] [Google Scholar]
- E. Kuwert and R. Schätzle, Gradient flow for the Willmore functional. Comm. Anal. Geom. 10 (2002) 307–339. [MathSciNet] [Google Scholar]
- E. Kuwert and R. Schätzle, Removability of point singularities of Willmore surfaces. Ann. Math. 160 (2004) 315–357. [CrossRef] [Google Scholar]
- M. Laradji and O.G. Mouritsen, Elastic properties of surfactant monolayers at liquid-liquid interfaces: A molecular dynamics study. J. Chem. Phys. 112 (2000) 8621–8630. [CrossRef] [Google Scholar]
- M. Leventon, O. Faugeraus and W. Grimson, Level set based segmentation with intensity and curvature priors, in Proceedings of Workshop on Mathematical Methods in Biomedical Image Analysis Proceedings (2000) 4–11. [Google Scholar]
- G.B. McFadden, A.A. Wheeler, R.J. Braun, S.R. Coriell and R.F. Sekerka, Phase-field models for anisotropic interfaces. Phys. Rev. E 48 (1993) 2016–2024. [Google Scholar]
- J. Melenkevitz and S.H. Javadpour, Phase separation dynamics in mixtures containing surfactants. J. Chem. Phys. 107 (1997) 623–629. [CrossRef] [Google Scholar]
- R. Rusu, An algorithm for the elastic flow of surfaces. Interfaces and Free Boundaries 7 (2005) 229–239. [Google Scholar]
- U. Seifert, Configurations of fluid membranes and vesicles. Adv. Phys. 46 (1997) 13–137. [CrossRef] [Google Scholar]
- L. Simon, Existence of surfaces minimizing the Willmore functional. Comm. Anal. Geom. 1 (1993) 281–326. [MathSciNet] [Google Scholar]
- G. Simonett, The Willmore flow near spheres. Differential Integral Equations 14 (2001) 1005–1014. [MathSciNet] [Google Scholar]
- J. Sokołowski and J.-P. Zolésio, Introduction to Shape Optimization, Springer Series in Computational Mathematics 16. Springer-Verlag, Berlin (1992). [Google Scholar]
- G. Sundaramoorthi, A. Yezzi, A. Mennucci and G. Sapiro, New possibilities with Sobolev active contours, in Proceedings of the 1st International Conference on Scale Space Methods and Variational Methods in Computer Vision (2007). [Google Scholar]
- J.E. Taylor, Crystalline variational problems. Bull. Amer. Math. Soc. 84 (1978) 568–588. [Google Scholar]
- J.E. Taylor, Mean curvature and weighted mean curvature. Acta Metall. Mater. 40 (1992) 1475–1485. [CrossRef] [Google Scholar]
- J.E. Taylor and J.W. Cahn, Linking anisotropic sharp and diffuse surface motion laws via gradient flows. J. Stat. Phys. 77 (1994) 183–197. [CrossRef] [Google Scholar]
- J.E. Taylor and J.W. Cahn, Diffuse interfaces with sharp corners and facets: Phase field modeling of strongly anisotropic surfaces. Physica D 112 (1998) 381–411. [CrossRef] [MathSciNet] [Google Scholar]
- S.L. Veatch and S.L. Keller, Separation of liquid phases in giant vesicles of ternary mixtures of phospholipids and cholesterol. Biophys. J. 85 (2003) 3074–3083. [CrossRef] [PubMed] [Google Scholar]
- A.A. Wheeler and G.B. McFadden, A ξ-vector formulation of anisotropic phase-field models: 3D asymptotics. Eur. J. Appl. Math. 7 (1996) 367–381. [Google Scholar]
- T.J. Willmore, Total curvature in Riemannian geometry. Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester (1982). [Google Scholar]
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