Free Access
Volume 46, Number 1, January-February 2012
Page(s) 59 - 79
Published online 22 July 2011
  1. 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]
  2. F. Almgren, J.E. Taylor and L. Wang, Curvature-driven flows: a variational approach. SIAM J. Control Optim. 31 (1993) 387–438. [Google Scholar]
  3. L. Ambrosio, Minimizing movements. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. 19 (1995) 191–246. [MathSciNet] [Google Scholar]
  4. 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]
  5. 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]
  6. M. Bauer and E. Kuwert, Existence of minimizing Willmore surfaces of prescribed genus. Int. Math. Res. Not. 10 (2003) 553–576. [CrossRef] [Google Scholar]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. 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]
  12. 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]
  13. 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]
  14. 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]
  15. 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]
  16. 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]
  17. 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]
  18. 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]
  19. M. Droske and M. Bertozzi, Higher-order feature-preserving geometric regularization. SIAM J. Imaging Sci. 3 (2010) 21–51. [CrossRef] [MathSciNet] [Google Scholar]
  20. G. Dziuk, Computational parametric Willmore flow. Numer. Math. 111 (2008) 55–80. [CrossRef] [MathSciNet] [Google Scholar]
  21. G. Dziuk, E. Kuwert and R. Schätzle, Evolution of elastic curves in Formula : existence and computation. SIAM J. Math. Anal. 33 (electronic) (2002) 1228–1245. [Google Scholar]
  22. 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]
  23. W. Helfrich, Elastic properties of lipid bilayers – theory and possible experiments. Zeitschrift Fur Naturforschung C-A J. Biosc. 28 (1973) 693. [Google Scholar]
  24. 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]
  25. 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]
  26. J.T. Jenkins, The equations of mechanical equilibrium of a model membrane. SIAM J. Appl. Math. 32 (1977) 755–764. [CrossRef] [MathSciNet] [Google Scholar]
  27. R. Keriven and O. Faugeras, Variational principles, surface evolution, PDEs, level set methods and the stereo problem. Technical Report 3021, INRIA (1996). [Google Scholar]
  28. 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]
  29. R. Kimmel and A.M. Bruckstein, Regularized Laplacian zero crossings as optimal edge integrators. IJCV 53 (2003) 225–243. [CrossRef] [Google Scholar]
  30. E. Kuwert and R. Schätzle, The Willmore flow with small initial energy. J. Differential Geom. 57 (2001) 409–441. [MathSciNet] [Google Scholar]
  31. E. Kuwert and R. Schätzle, Gradient flow for the Willmore functional. Comm. Anal. Geom. 10 (2002) 307–339. [MathSciNet] [Google Scholar]
  32. E. Kuwert and R. Schätzle, Removability of point singularities of Willmore surfaces. Ann. Math. 160 (2004) 315–357. [CrossRef] [Google Scholar]
  33. 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]
  34. 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]
  35. 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]
  36. J. Melenkevitz and S.H. Javadpour, Phase separation dynamics in mixtures containing surfactants. J. Chem. Phys. 107 (1997) 623–629. [CrossRef] [Google Scholar]
  37. R. Rusu, An algorithm for the elastic flow of surfaces. Interfaces and Free Boundaries 7 (2005) 229–239. [Google Scholar]
  38. U. Seifert, Configurations of fluid membranes and vesicles. Adv. Phys. 46 (1997) 13–137. [CrossRef] [Google Scholar]
  39. L. Simon, Existence of surfaces minimizing the Willmore functional. Comm. Anal. Geom. 1 (1993) 281–326. [MathSciNet] [Google Scholar]
  40. G. Simonett, The Willmore flow near spheres. Differential Integral Equations 14 (2001) 1005–1014. [MathSciNet] [Google Scholar]
  41. J. Sokołowski and J.-P. Zolésio, Introduction to Shape Optimization, Springer Series in Computational Mathematics 16. Springer-Verlag, Berlin (1992). [Google Scholar]
  42. 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]
  43. J.E. Taylor, Crystalline variational problems. Bull. Amer. Math. Soc. 84 (1978) 568–588. [Google Scholar]
  44. J.E. Taylor, Mean curvature and weighted mean curvature. Acta Metall. Mater. 40 (1992) 1475–1485. [CrossRef] [Google Scholar]
  45. 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]
  46. 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]
  47. 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]
  48. 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]
  49. T.J. Willmore, Total curvature in Riemannian geometry. Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester (1982). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you