On the areas of genus zero free boundary minimal surfaces embedded in the unit 3-ball. (English) Zbl 07880818
Reviewer: Ergin Bayram (Samsun)
Found 76 Documents (Results 1–76)
Generalized minimizing movements for the varifold Canham-Helfrich flow. (English) Zbl 07874989
Reviewer: Dimitris P. Vartziotis (Ioannina)
A boundary maximum principle for stationary pairs of varifolds with fixed contact angle. (English) Zbl 1541.53080
A structure theory for stable codimension 1 integral varifolds with applications to area minimising hypersurfaces mod \(p\). (English) Zbl 1542.53016
Reviewer: Cristian Chifu (Cluj-Napoca)
Boundary regularity for anisotropic minimal Lipschitz graphs. (English) Zbl 1539.49036
Reviewer: Uwe Prüfert (Freiberg)
On the existence of canonical multi-phase Brakke flows. (English) Zbl 1533.53077
Reviewer: Igor Bock (Bratislava)
Hypersurfaces with mean curvature prescribed by an ambient function: compactness results. (English) Zbl 1529.53009
Reviewer: Giorgio Saracco (Firenze)
The existence of a weak solution to volume preserving mean curvature flow in higher dimensions. (English) Zbl 07687726
Recovering the homology of immersed manifolds. (English) Zbl 1528.55005
Reviewer: Semra Pamuk (Ankara)
First stability eigenvalue of singular hypersurfaces with constant mean curvature in the unit sphere. (English) Zbl 1506.53006
On Brakke’s mean curvature flow. (English) Zbl 07735873
Sugaku Expo. 35, No. 2, 243-264 (2022); translation from Sūgaku 71, No. 2, 138-158 (2019).
Reviewer: Emil Saucan (Karmiel)
A barrier principle at infinity for varifolds with bounded mean curvature. (English) Zbl 07730378
Reviewer: Giovanni Anello (Messina)
Regularity of free boundary minimal surfaces in locally polyhedral domains. (English) Zbl 1498.49076
Reviewer: Giorgio Saracco (Trento)
Regularity of minimal and CMC stable hypersurfaces: a brief overview. (English) Zbl 1470.53004
Giga, Yoshikazu (ed.) et al., The role of metrics in the theory of partial differential equations. Proceedings of the 11th Mathematical Society of Japan, Seasonal Institute (MSJ-SI), Nagoya University, Japan, July 2–13 2018. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 85, 491-511 (2021).
The Canham-Helfrich model for the elasticity biomembranes as a limit of mesoscopic energiess. (English) Zbl 1471.49010
Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 21st international conference on geometry, integrability and quantization, Varna, Bulgaria, June 3–8, 2019. Sofia: Avangard Prima; Sofia: Bulgarian Academy of Sciences, Institute of Biophysics and Biomedical Engineering. Geom. Integrability Quantization 21, 170-180 (2020).
Infinitely many minimal surfaces in low dimensions [after F. C. Marques, A. A. Neves et A. Song]. (Infinité d’hypersurfaces minimales en basses dimensions [d’après F. C. Marques, A. A. Neves et A. Song].) (French. English summary) Zbl 1476.53013
Séminaire Bourbaki. Volume 2018/2019, Exposés 1151–1165. Avec table par noms d’auteurs de 1948 à 2018/19. Paris: Société Mathématique de France (SMF). Astérisque 422, 499-543, Exp. No. 1165 (2020).
The regularity of parametrized integer stationary varifolds in two dimensions. (English) Zbl 1512.49039
Reviewer: Savin Treanta (Bucureşti)
A varifold perspective on the \(p\)-elastic energy of planar sets. (English) Zbl 1446.49032
Reviewer: Stepan Agop Tersian (Rousse)
Convergence of solutions of some Allen-Cahn equations to Brakke’s mean curvature flow. (English) Zbl 1448.35307
Existence of varifold minimizers for the multiphase Canham-Helfrich functional. (English) Zbl 1439.49074
Reviewer: Stepan Agop Tersian (Rousse)
Soap films with gravity and almost-minimal surfaces. (English) Zbl 1431.49047
Reviewer: Gabriel Eduard Vilcu (Ploieşti)
Allard’s interior regularity theorem: an invitation to stationary varifolds. (English) Zbl 1517.49027
Bieri, Lydia (ed.) et al., Nonlinear analysis in geometry and applied mathematics. Part 2. Based on lectures presented during the program year 2015–2016 on “Nonlinear Equations” at the Harvard Center of Mathematical Sciences and Applications, Cambridge, MA, USA. Somerville, MA: International Press. Harv. Univ. CMSA Ser. Math. 2, 23-49 (2018).
Convergence of solutions of the weighted Allen-Cahn equations to Brakke type flow. (English) Zbl 1428.35180
The concept of varifold. (English) Zbl 1380.49064
Discrete varifolds and surface approximation. (English) Zbl 1380.49037
Bergounioux, Maïtine (ed.) et al., Topological optimization and optimal transport in the applied sciences. Berlin: De Gruyter (ISBN 978-3-11-043926-7/hbk; 978-3-11-043041-7/ebook). Radon Series on Computational and Applied Mathematics 17, 159-170 (2017).
Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds. (English) Zbl 1377.49049
Geometric measure theory. A beginner’s guide. Illustrated by James F. Bredt. 5th edition. (English) Zbl 1338.49089
Amsterdam: Elsevier/Academic Press (ISBN 978-0-12-804489-6). viii, 263 p. (2016).
Discrete varifolds: a unified framework for discrete approximations of surfaces and mean curvature. (English) Zbl 1450.65016
Aujol, Jean-François (ed.) et al., Scale space and variational methods in computer vision. 5th international conference, SSVM 2015, Lège-Cap Ferret, France, May 31 – June 4, 2015. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9087, 513-524 (2015).
MSC:
65D17
Allen-Cahn approximation of mean curvature flow in Riemannian manifolds. II: Brakke’s flows. (English) Zbl 1336.53083
Reviewer: Jan Swoboda (München)
Existence of integral \(m\)-varifolds minimizing \(\int |A|^p\) and \(\int |H|^p\), \(p>m\), in Riemannian manifolds. (English) Zbl 1282.49041
Varifolds and generalized curvature. (English. French summary) Zbl 1334.49141
Quantitative stratification and the regularity of mean curvature flow. (English) Zbl 1277.53064
Reviewer: Alina Stancu (Montréal)
MSC:
53C44
A convergence theorem for immersions with \(L^2\)-bounded second fundamental form. (English) Zbl 1254.53091
Reviewer: Themistocles M. Rassias (Athens)
MSC:
53C42
Currents and curvature varifolds in continuum mechanics. (English) Zbl 1235.49080
Arkhipova, Aina A. (ed.) et al., Nonlinear partial differential equations and related topics. Dedicated to Nina U. Uraltseva on the occasion of her 75th birthday. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4997-2/hbk). Translations. Series 2. American Mathematical Society 229; Advances in the Mathematical Sciences 64, 97-117 (2010).
Physical significance of the curvature varifold-based description of crack nucleation. (English) Zbl 1231.74382
Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 21, No. 2, 215-233 (2010).
Currents and flat chains associated to varifolds, with an application to mean curvature flow. (English) Zbl 1161.49043
MSC:
49Q15
53C44
Geometric measure theory. A beginner’s guide. Illustrated by James F. Bredt. 4th ed. (English) Zbl 1179.49050
Amsterdam: Elsevier/Academic Press (ISBN 978-0-12-374444-9/hbk). viii, 249 p. (2009).
Reviewer: Andrew Bucki (Edmond)
Uniform rectifiability from mean curvature bounds. (English) Zbl 1152.35052
Chen, Chiun-Chuan (ed.) et al., Recent advances in elliptic and parabolic problems. Proceedings of the international conference, Hsinchu, Taiwan, February 16–20, 2004. Hackensack, NJ: World Scientific (ISBN 981-256-189-7/hbk). 197-201 (2005).
On the singularities and a Bernstein property of immersed stable minimal hypersurfaces. (English) Zbl 1067.53049
Reviewer: Wayne Rossman (Kobe)
Quadratic tilt-excess decay and strong maximum principle for varifolds. (English) Zbl 1096.49023
Reviewer: Michele Miranda (Lecce)
A direct variational approach to a problem arising in image reconstruction. (English) Zbl 1029.49037
Geometric measure theory. A beginner’s guide. 3rd ed. (English) Zbl 0974.49025
San Diego, CA: Academic Press. x, 226 p. (2000).
Reviewer: H.Parks (Corvallis)
Minimal surfaces. (English) Zbl 0987.49025
Courant Lecture Notes in Mathematics. 4. New York, NY: Courant Institute of Mathematical Sciences. viii, 124 p. (1999).
Approximation problems for curvature varifolds. (English) Zbl 0932.58013
Reviewer: M.Fuchs (Saarbrücken)
MSC:
58E15
The mean curvature integral is invariant under bending. (English) Zbl 0914.53007
Rivin, Igor (ed.) et al., The Epstein Birthday Schrift dedicated to David Epstein on the occasion of his 60th birthday. Warwick: University of Warwick, Institute of Mathematics, Geom. Topol. Monogr. 1, 1-21 (1998).
Reviewer: B.Opozda (Kraków)
Sharp isoperimetric inequalities for stationary varifolds and area minimizing flat chains \(\text{mod} k\). (English) Zbl 0867.53006
Reviewer: G.Philippin (Quebec)
A strong maximum principle for singular minimal hypersurfaces. (English) Zbl 0863.49030
Reviewer: C.Bär (Freiburg)
Geometric measure theory. A beginner’s guide. 2nd ed. (English) Zbl 0819.49024
San Diego, CA: Academic Press (ISBN 0-12-506857-3). ix, 173 p. (1995).
Oriented and nonoriented curvature varifolds. (English) Zbl 0821.49029
Reviewer: H.Parks (Corvallis)
MSC:
49Q15
Motion of level sets by mean curvature. IV. (English) Zbl 0829.53040
Reviewer: U.Hamenstädt (Bonn)
A general existence theorem for integral currents with prescribed mean curvature form. (English) Zbl 0786.49025
Reviewer: F.Duzaar (Bonn)
The Plateau problem. Part I: Historical survey. Part II: The present state of the theory. Transl. from the Russian by Oleg Efimov. (English) Zbl 0729.53001
Studies in the Development of Modern Mathematics, 1. New York etc.: Gordon and Breach Science Publishers. xii, 220 p./pt.1; xii, 251 p./pt.2; $ 175.00/pt.1; $ 175.00/pt.2; $ 245.00/set (1990).
Reviewer: F.Tomi (Heidelberg)
On the existence of integral currents with prescribed mean curvature vector. (English) Zbl 0703.49035
Area-minimizing hypersurfaces defined by homotopy classes of mappings of 1-essential manifolds. (English) Zbl 0711.49063
Reviewer: F.Tomi
Das Existenzproblem für Minimalflächen. (The existence problem for minimal surfaces). (German) Zbl 0665.53007
Reviewer: F.Tomi
Geometric measure theory. A beginner’s guide. (English) Zbl 0671.49043
Boston, MA etc.: Academic Press, Inc. viii, 145 p. $ 19.95 (1988).
Reviewer: Michael Grüter (Saarbrücken)
Minimal surfaces and the Plateau problem. (Minimal’nye poverkhnosti i problema Plato). (Russian) Zbl 0617.53001
Moskva: “Nauka”. Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 312 p. R. 3.90 (1987).
Reviewer: J.Weinstein
Boundary regularity for solutions of a partitioning problem. (English) Zbl 0613.49029
Reviewer: M.Fuchs
Optimal regularity for codimension one minimal surfaces with a free boundary. (English) Zbl 0609.35012
Regularity theorems for varifolds with mean curvature. (English) Zbl 0595.49029
Reviewer: H.Parks
Curvature estimates for minimal surfaces in 3-manifolds. (English) Zbl 0578.49027
Reviewer: H.Parks
Minimising curvature. A higher dimensional analogue of the Plateau problem. (English) Zbl 0592.53003
Nonlinear analysis, Miniconf. Canberra/Aust. 1984, Proc. Cent. Math. Anal. Aust. Natl. Univ. 8, 113-122 (1984).
Reviewer: H.Parks
Survey lectures on minimal submanifolds. (English) Zbl 0541.53045
Semin. on minimal submanifolds, Ann. Math. Stud. 103, 3-52 (1983).
Reviewer: K.Leichtweiß
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