Mean Curvature Flow of Mean Convex Hypersurfaces
By Robert Haslhofer, Bruce Kleiner. 2013
168 citations recorded by the source corpus.
In the last 15 years, White and Huisken‐Sinestrari developed a far‐reaching structure theory for the mean curvature flow of mean convex hypersurfaces. Their papers provide a package of estimates and structural results that yield a precise description of singularities and of high‐curvature regions in a mean convex flow.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/143755efbf6a78897bf9e5cb5547253d7da75c17
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In Applied Mathematics
- Robert Haslhofer
- G. Huisken
- Bruce Kleiner
- S. Brendle
- Kyeongsu Choi
- Or Hershkovits
- Carlo Sinestrari
- B. White
In Geometry and Topology
- Robert Haslhofer
- Bruce Kleiner
- S. Brendle
- G. Huisken
- Kyeongsu Choi
- Or Hershkovits
- B. White
- Carlo Sinestrari
Citations in the corpus
- Ancient asymptotically cylindrical flows and applications (2019, background): “If x′ ∈ N′ t′ is a singular point, then by [HK17a] and the entropy assumption, the singularity at (x′, t′) is spherical.”
- Convex ancient solutions of the mean curvature flow (2014, methodology): “We recall that for mean convex noncollapsed solutions, not necessarily ancient nor k-convex, Haslhofer and Kleiner [13] have proved a gradient estimate of the form (5.14), with C also depending on the constant in the noncollapsing condition.”
- Mean curvature flow with surgery of mean convex surfaces in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb (2013, methodology): “To get around this issue, we combine the interior gradient estimate established in [10] with a new pseudolocality principle for the mean curvature flow (cf.”
- Complete translating solitons to the mean curvature flow in ℝ3 with nonnegative mean curvature (2020, background): “The α-noncollapsed condition is a deep and powerful property of weak solutions of the mean convex mean curvature flow [17, 36] which implies that any complete (α-noncollapsed) mean convex translating soliton Σ is convex with uniformly bounded second fundamental form.”
- Mean curvature flow with surgery (2014, methodology): “In the proof of the convexity estimate and the global curvature estimate, we then follow closely the scheme from our previous paper [HK13a], highlighting the new steps necessitated by surgeries.”