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Construction of solutions for some localized nonlinear Schrödinger equations
Existence of self-similar solutions of the inverse mean curvature flow
Institute of Mathematics, Academia Sinica, Taipei, Taiwan |
We will give a new proof of a recent result of P. Daskalopoulos, G. Huisken and J.R. King ([
References:
[1] |
B. Allen, Non-compact Solutions to Inverse Mean Curvature Flow in Hyperbolic Space, Ph.D. thesis, University of Tennessee, Knoxville, USA, 2016. |
[2] |
P. Daskalopoulos and G. Huisken, Inverse mean curvature flow of entire graphs, arXiv: 1709.06665v1 |
[3] |
C. Gerhardt,
Flow of nonconvex hypersurfaces into spheres, J. Differential Geom., 32 (1990), 299-314.
|
[4] |
G. Huisken and T. Ilmanen,
The Riemannian Penrose inequality, Internat. Math. Res. Notices, 20 (1997), 1045-1058.
doi: 10.1155/S1073792897000664. |
[5] |
G. Huisken and T. Ilmanen,
The inverse mean curvature flow and the Riemannian Penrose inequality, J. Differential Geom., 59 (2001), 353-437.
|
[6] |
G. Huisken and T. Ilmanen,
Higher regularity of the inverse mean curvature flow, J. Differential Geom., 80 (2008), 433-451.
|
[7] |
B. Lambert and J. Scheuer,
The inverse mean curvature flow perpendicular to the sphere, Math. Ann., 364 (2016), 1069-1093.
doi: 10.1007/s00208-015-1248-2. |
[8] |
T. Marquardt,
Inverse mean curvature flow for star-shaped hypersurfaces evolving in a cone, J. Geom. Anal., 23 (2013), 1303-1313.
doi: 10.1007/s12220-011-9288-7. |
[9] |
T. Marquardt,
Weak solutions of the inverse mean curvature flow for hypersurfaces with boundary, J. Reine Angew. Math., 728 (2017), 237-261.
doi: 10.1515/crelle-2014-0116. |
[10] |
K. Smoczyk,
Remarks on the inverse mean curvature flow, Asian J. Math., 4 (2000), 331-335.
doi: 10.4310/AJM.2000.v4.n2.a3. |
[11] |
J. Urbas,
On the expansion of starshaped hypersurfaces by symmetric functions of their principle curvatures, Math. Z., 205 (1990), 355-372.
doi: 10.1007/BF02571249. |
show all references
References:
[1] |
B. Allen, Non-compact Solutions to Inverse Mean Curvature Flow in Hyperbolic Space, Ph.D. thesis, University of Tennessee, Knoxville, USA, 2016. |
[2] |
P. Daskalopoulos and G. Huisken, Inverse mean curvature flow of entire graphs, arXiv: 1709.06665v1 |
[3] |
C. Gerhardt,
Flow of nonconvex hypersurfaces into spheres, J. Differential Geom., 32 (1990), 299-314.
|
[4] |
G. Huisken and T. Ilmanen,
The Riemannian Penrose inequality, Internat. Math. Res. Notices, 20 (1997), 1045-1058.
doi: 10.1155/S1073792897000664. |
[5] |
G. Huisken and T. Ilmanen,
The inverse mean curvature flow and the Riemannian Penrose inequality, J. Differential Geom., 59 (2001), 353-437.
|
[6] |
G. Huisken and T. Ilmanen,
Higher regularity of the inverse mean curvature flow, J. Differential Geom., 80 (2008), 433-451.
|
[7] |
B. Lambert and J. Scheuer,
The inverse mean curvature flow perpendicular to the sphere, Math. Ann., 364 (2016), 1069-1093.
doi: 10.1007/s00208-015-1248-2. |
[8] |
T. Marquardt,
Inverse mean curvature flow for star-shaped hypersurfaces evolving in a cone, J. Geom. Anal., 23 (2013), 1303-1313.
doi: 10.1007/s12220-011-9288-7. |
[9] |
T. Marquardt,
Weak solutions of the inverse mean curvature flow for hypersurfaces with boundary, J. Reine Angew. Math., 728 (2017), 237-261.
doi: 10.1515/crelle-2014-0116. |
[10] |
K. Smoczyk,
Remarks on the inverse mean curvature flow, Asian J. Math., 4 (2000), 331-335.
doi: 10.4310/AJM.2000.v4.n2.a3. |
[11] |
J. Urbas,
On the expansion of starshaped hypersurfaces by symmetric functions of their principle curvatures, Math. Z., 205 (1990), 355-372.
doi: 10.1007/BF02571249. |
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