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Time-like surfaces of prescribed anisotropic mean curvature in Minkowski space
1. | Institut für Differentialgeometrie, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany, Germany |
[1] |
Chiara Corsato, Franco Obersnel, Pierpaolo Omari, Sabrina Rivetti. On the lower and upper solution method for the prescribed mean curvature equation in Minkowski space. Conference Publications, 2013, 2013 (special) : 159-169. doi: 10.3934/proc.2013.2013.159 |
[2] |
Hongjie Ju, Jian Lu, Huaiyu Jian. Translating solutions to mean curvature flow with a forcing term in Minkowski space. Communications on Pure and Applied Analysis, 2010, 9 (4) : 963-973. doi: 10.3934/cpaa.2010.9.963 |
[3] |
Qinian Jin, YanYan Li. Starshaped compact hypersurfaces with prescribed $k$-th mean curvature in hyperbolic space. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 367-377. doi: 10.3934/dcds.2006.15.367 |
[4] |
Alessio Pomponio. Oscillating solutions for prescribed mean curvature equations: euclidean and lorentz-minkowski cases. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 3899-3911. doi: 10.3934/dcds.2018169 |
[5] |
Ruyun Ma, Man Xu. Connected components of positive solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space. Discrete and Continuous Dynamical Systems - B, 2019, 24 (6) : 2701-2718. doi: 10.3934/dcdsb.2018271 |
[6] |
Daniela Gurban, Petru Jebelean, Cǎlin Şerban. Non-potential and non-radial Dirichlet systems with mean curvature operator in Minkowski space. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 133-151. doi: 10.3934/dcds.2020006 |
[7] |
Georgi I. Kamberov. Recovering the shape of a surface from the mean curvature. Conference Publications, 1998, 1998 (Special) : 353-359. doi: 10.3934/proc.1998.1998.353 |
[8] |
Yi Zhou, Jianli Liu. The initial-boundary value problem on a strip for the equation of time-like extremal surfaces. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 381-397. doi: 10.3934/dcds.2009.23.381 |
[9] |
Oleksandr Misiats, Nung Kwan Yip. Convergence of space-time discrete threshold dynamics to anisotropic motion by mean curvature. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6379-6411. doi: 10.3934/dcds.2016076 |
[10] |
Xinqun Mei, Jundong Zhou. The interior gradient estimate of prescribed Hessian quotient curvature equation in the hyperbolic space. Communications on Pure and Applied Analysis, 2021, 20 (3) : 1187-1198. doi: 10.3934/cpaa.2021012 |
[11] |
Chiara Corsato, Colette De Coster, Franco Obersnel, Pierpaolo Omari, Alessandro Soranzo. A prescribed anisotropic mean curvature equation modeling the corneal shape: A paradigm of nonlinear analysis. Discrete and Continuous Dynamical Systems - S, 2018, 11 (2) : 213-256. doi: 10.3934/dcdss.2018013 |
[12] |
Franco Obersnel, Pierpaolo Omari. On a result of C.V. Coffman and W.K. Ziemer about the prescribed mean curvature equation. Conference Publications, 2011, 2011 (Special) : 1138-1147. doi: 10.3934/proc.2011.2011.1138 |
[13] |
Yoshikazu Giga, Yukihiro Seki, Noriaki Umeda. On decay rate of quenching profile at space infinity for axisymmetric mean curvature flow. Discrete and Continuous Dynamical Systems, 2011, 29 (4) : 1463-1470. doi: 10.3934/dcds.2011.29.1463 |
[14] |
Elias M. Guio, Ricardo Sa Earp. Existence and non-existence for a mean curvature equation in hyperbolic space. Communications on Pure and Applied Analysis, 2005, 4 (3) : 549-568. doi: 10.3934/cpaa.2005.4.549 |
[15] |
Guido De Philippis, Antonio De Rosa, Jonas Hirsch. The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals. Discrete and Continuous Dynamical Systems, 2019, 39 (12) : 7031-7056. doi: 10.3934/dcds.2019243 |
[16] |
Matteo Novaga, Enrico Valdinoci. Closed curves of prescribed curvature and a pinning effect. Networks and Heterogeneous Media, 2011, 6 (1) : 77-88. doi: 10.3934/nhm.2011.6.77 |
[17] |
Yong Huang, Lu Xu. Two problems related to prescribed curvature measures. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 1975-1986. doi: 10.3934/dcds.2013.33.1975 |
[18] |
Huyuan Chen, Dong Ye, Feng Zhou. On gaussian curvature equation in $ \mathbb{R}^2 $ with prescribed nonpositive curvature. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3201-3214. doi: 10.3934/dcds.2020125 |
[19] |
Yoshikazu Giga, Hiroyoshi Mitake, Hung V. Tran. Remarks on large time behavior of level-set mean curvature flow equations with driving and source terms. Discrete and Continuous Dynamical Systems - B, 2020, 25 (10) : 3983-3999. doi: 10.3934/dcdsb.2019228 |
[20] |
Alberto Boscaggin, Francesca Colasuonno, Benedetta Noris. Positive radial solutions for the Minkowski-curvature equation with Neumann boundary conditions. Discrete and Continuous Dynamical Systems - S, 2020, 13 (7) : 1921-1933. doi: 10.3934/dcdss.2020150 |
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