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Motion of level sets by mean curvature. I
Open accessAbstract
We construct a unique weak solution of the nonlinear PDE which asserts each level set evolves in time according to its mean curvature.This weak solution allows us then to define for any compact set Γ o a unique generalized motion by mean curvature, existing for all time.We investigate the various geometric properties and pathologies of this evolution.
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Cited by
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
Vese, L. A., & Chan, T. F. (2002) · International Journal of Computer Vision · doi:10.1023/a:1020874308076 · Cited by 2,384
A PDE-Based Fast Local Level Set Method
Peng, D., Merriman, B., Osher, S., Zhao, H., & Kang, M. (1999) · Journal of Computational Physics · doi:10.1006/jcph.1999.6345 · Cited by 1,255
The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality
Huisken, G., & Ilmanen, T. (2001) · Journal of Differential Geometry · doi:10.4310/jdg/1090349447 · Cited by 463
Hensel, S., & Laux, T. (2025) · Journal of Differential Geometry · doi:10.4310/jdg/1747065796 · Cited by 25
End-time regularity theorem for Brakke flows
Stuvard, S., & Tonegawa, Y. (2024) · Mathematische Annalen · doi:10.1007/s00208-024-02826-8 · Cited by 7
Metadata
- Authors
- Evans, L. C., & Spruck, J.
- Venue
- Journal of Differential Geometry
- Publisher
- International Press of Boston
- Published
- 1991-01-01
- Volume
- 33
- Issue
- 3
- ISSN
- 0022-040X (ISSN-L)
- OpenAlex
- W2082052570
- Cited by
- 1,158
- References
- 0
- FWCI
- 55.01
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Evans, L. C., & Spruck, J. (1991). Motion of level sets by mean curvature. I. Journal of Differential Geometry. https://doi.org/10.4310/jdg/1214446559
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