Free Access
Issue |
ESAIM: COCV
Volume 27, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|
|
---|---|---|
Article Number | S2 | |
Number of page(s) | 35 | |
DOI | https://doi.org/10.1051/cocv/2020049 | |
Published online | 01 March 2021 |
- M. Abate and F. Tovena, Curve e Superfici. Springer, Italia (2006). [Google Scholar]
- R. Alessandroni and E. Kuwert, Local solutions to a free boundary problem for the Willmore functional. Calc. Var. Partial Differ. Equ. 55 (2016) 24. [Google Scholar]
- L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Science Publications (2000). [Google Scholar]
- M. Bauer and E. Kuwert, Existence of minimizing Willmore surfaces of prescribed genus. Int. Math. Res. Notices 10 (2003) 553–576. [Google Scholar]
- M. Bergner, A. Dall’Acqua and S. Fröhlich, Symmetric Willmore surfaces of revolution satisfying natural boundary conditions. Calc. Var. Partial Differ. Equ. 39 (2010) 361–378. [Google Scholar]
- M. Bergner, A. Dall’Acqua and S. Fröhlich, Willmore surfaces of revolution with two prescribed boundary circles. J. Geometric Anal. 23 (2013) 283–302. [Google Scholar]
- B. Chen, Some conformal invariants of submanifolds and their applications. Bollettino dell’Unione Matematica Italiana 10 (1974) 380–385. [Google Scholar]
- F. Da Lio, F. Palmurella and T. Rivière, A resolution of the poisson problems for elastic plates. Arch. Ration. Mech. Anal. 236 (2020) 1593–1676. [Google Scholar]
- A. Dall’Acqua, Uniqueness for the homogeneous Dirichlet Willmore boundary value problem. Ann. Global Anal. Geom. 42 (2012) 411–420. [Google Scholar]
- A. Dall’Acqua, K. Deckelnick and H. Grunau, Classical solutions to the Dirichlet problem for Willmore surfaces of revolution. Adv. Calc. Var. 1 (2008) 379–397. [Google Scholar]
- A. Dall’Acqua, K. Deckelnick and G. Wheeler, Unstable Willmore surfaces of revolution subject to natural boundary conditions. Calc. Var. Partial Differ. Equ. 48 (2013) 293–313. [Google Scholar]
- A. Dall’Acqua, S. Fröhlich, H. Grunau and F. Schieweck, Symmetric Willmore surfaces of revolution satisfying arbitrary Dirichlet boundary data. Adv. Calc. Var. 4 (2011) 1–81. [Google Scholar]
- K. Deckelnick and H. Grunau, A Navier boundary value problem for Willmore surfaces of revolution. Analysis (Munich) 29 (2009) 229–258. [Google Scholar]
- K. Deckelnick, H. Grunau and M. Röger, Minimising a relaxed Willmore functional for graphs subject to boundary conditions. Interfaces Free Bound. 19 (2017) 109–140. [Google Scholar]
- U. Dierkes, S. Hildebrandt and A.J. Tromba, Global Analysis of Minimal Surfaces. Springer (2010). [Google Scholar]
- S. Eichmann, Nonuniqueness for Willmore surfaces of revolution satisfying dirichlet boundary data. J. Geom. Anal. 26 (2016) 2563–2590. [Google Scholar]
- S. Eichmann, The Helfrich boundary value problem. Calc. Var. Partial Differ. Equ. 58 (2019) 34. [Google Scholar]
- S. Eichmann and H. Grunau, Existence for Willmore surfaces of revolution satisfying non-symmetric Dirichlet boundary conditions. Adv. Calc. Var. 12 (2019) 333–361. [Google Scholar]
- J. Hutchinson, Second fundamental form for varifolds and the existence of surfaces minimizing curvature. Indiana Univ. Math. J. 35 (1986) 45–71. [Google Scholar]
- E. Kuwert and R. Schätzle, Removability of point singularities of Willmore surfaces. Ann. Math. 160 (2004) 315–357. [Google Scholar]
- J. Langer, A compactness theorem for sirfaces with Lp-bounded second fundamental form. Math. Ann. 270 (1985) 223–234. [Google Scholar]
- T. Liimatainen and M. Salo, n-harmonic coordinates and the regularity of conformal mappings. Math. Res. Lett. 21 (2014) 341–361. [Google Scholar]
- R. Mandel, Explicit formulas, symmetry and symmetry breaking for Willmore surfaces of revolution. Ann. Glob. Anal. Geom. 54 (2018) 187–236. [Google Scholar]
- C. Mantegazza, Curvature varifolds with boundary. J. Differ. Geometry 43 (1996) 807–843. [Google Scholar]
- A. Mondino and C. Scharrer, Existence and regularity of spheres minimising the Canham-Helfrich energy. Arch. Ration. Mech. Anal. 236 (2020) 1455–1485. [Google Scholar]
- J. Nitsche, Boundary value problems for variational integrals involving surface curvatures. Quart. Appl. Math. 51 (1993) 363–387. [Google Scholar]
- M. Novaga and M. Pozzetta, Connected surfaces with boundary minimizing the Willmore energy. Math. Eng. 2 (2020) 527–556. [Google Scholar]
- B. Palmer, Uniqueness theorems for Willmore surfaces with fixed and free Boundaries. Indiana Univ. Math. J. 49 (2000) 1581–1601. [Google Scholar]
- J. Pitts, Existence and regularity of minimal surfaces on riemannian manifolds. Mathematical Notes. Princeton University Press (1981). [Google Scholar]
- M. Pozzetta, Ph.D. thesis, Università di Pisa. Inpreparation (2020). [Google Scholar]
- T. Rivière, Analysis aspects of Willmore surfaces. Invent. Math. 174 (2008) 1–45. [Google Scholar]
- T. Rivière, Lipschitz conformal immersions fromdegenerating Riemann surfaces with L2 -bounded second fundamental forms. Adv. Calc. Var. 6 (2013) 1–31. [Google Scholar]
- T. Rivière, Variational principles for immersed surfaces with L2-bounded second fundamental form. J. für die reine Angew. Math. 695 (2014) 41–98. [Google Scholar]
- R. Schätzle, The Willmore boundary problem. Calc. Var. 37 (2010) 275–302. [Google Scholar]
- J. Schygulla, Willmore minimizers with prescribed isoperimetric ratio. Arch. Ration. Mech. Anal. 203 (2012) 901–941. [Google Scholar]
- L. Simon, Lectures on geometric measure theory. Proc. Centre Math. Anal. Austr. Natl. Univ. (1984). [Google Scholar]
- L. Simon, Existence of surfaces minimizing the Willmore functional. Commun. Anal. Geometry 1 (1993) 281–326. [Google Scholar]
- M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. 3, Third Edition, Publish or Perish, Houston, Texas (1999). [Google Scholar]
- J.L. Weiner, On a problem of Chen, Willmore, et al. Indiana Univ. Math. J. 27 (1978) 19–35. [Google Scholar]
- T.J. Willmore, Note on embedded surfaces. Ann. Alexandru Cuza Univ. Section I 11B (1965) 493–496. [Google Scholar]
- T.J. Willmore, Riemannian Geometry. Oxford Science Publications (1993). [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.