The inverse mean curvature flow and the Riemannian Penrose Inequality

By G. Huisken, T. Ilmanen. 2001

965 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/d072f082b96ace3d530ad6738113bd2f8863e2f1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. M. Mars
2. A. Neves
3. Junfang Li
4. Pengfei Guan
5. Dan A. Lee
6. Mihalis Dafermos
7. Chun-Lei He
8. B. Krishnan

In Astronomy and Astrophysics

1. M. Mars
2. Igor Rodnianski
3. Mihalis Dafermos
4. Abhay Ashtekar
5. A. Neves
6. B. Krishnan
7. David Garfinkle
8. J. Senovilla

Citations in the corpus

• Ricci flow on asymptotically Euclidean manifolds (2016, methodology): “In 2001, Huisken and Ilmanen [21] proved the stronger Riemannian Penrose inequality in dimension three by using the inverse mean curvature flow.”
• Nonlinear evolution by mean curvature and isoperimetric inequalities (2006, methodology): “Ilmanen developed a weak level set formulation for the inverse mean curvature flow to prove the Riemannian Penrose inequality in [10].”
• The 1965 Penrose singularity theorem (2014, background): “However, (14) has been proven in the so-called Riemannian case [185, 47] which, from the space-time viewpoint,”
• Isolated and Dynamical Horizons and Their Applications (2004, background): “The conjecture has been proved in time symmetric situations relatively recently [101, 52].”
• Lectures on black holes and linear waves (2008, background): “See the important papers of HuiskenIlmanen [95] and Bray [25].”
• Classification of prime 3-manifolds with σ-invariant greater than RP 3 (2004, methodology): “[7] G. Huisken and T. Ilmanen, The inverse mean curvature flow and the Riemannian Penrose inequality, J. Differential Geom.”
• The phase field method for geometric moving interfaces and their numerical approximations (2019, positive): “In [266] Huisken and Ilmanen proposed a sub-level set formulation for the inverse mean curvature flow (IMCF), as expected, this formulation does not have the form of the general level set equation (3), which would give the following unusual PDE:”
• The inverse mean curvature flow and p-harmonic functions (2007, methodology): “Another result of [4] states that proper weak solutions of the problem are unique.”
• The quermassintegral inequalities for k-convex starshaped domains (2009, background): “There is a notion of weak solution studied by Huisken-Ilmanen for the Penrose inequality in [ 11 ].”
• The evolution problem in general relativity (2008, background): “See the important papers of Huisken-Ilmanen [86] and Bray [22].”
• Existence, Regularity, and Properties of Generalized Apparent Horizons (2008, background): “In this section we give the proof of Conjecture 1. The outermost generalized apparent horizon is constructed as the boundary of the union of all generalized trapped subdomains in . This is consistent with the construction of the apparent horizon as the boundary of the trapped region (see [HE73], [KH”