Isoperimetric regions in cones

By Frank Morgan, M. Ritoré. 2002

65 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/f3e9d4b2003eed4d6559cea7d5966f595041bb0d

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In Applied Mathematics

In Astronomy and Astrophysics

Citations in the corpus

Intrinsic structure of minimal discs in metric spaces (2016, background): “The first example is well known; see [28].”
Area Minimizing Discs in Metric Spaces (2015, background): “Then X is a complete metric space admitting a global quadratic isoperimetric inequality with constant C = 1 4πr for any definition of volume μ, see for example [45].”
Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones (2003, methodology): “Hence, the proof finishes if we prove that I(u, u) > 0. To prove this inequality, we can proceed as i n [MR], Lemma 3.3.”
Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds (2015, background): “Let us also mention that the isoperimetric problem has already been studied in presence of (mild) singularities of the space: mostly for conical manifolds [49, 53] and polytopes [52].”
The hyperplane is the only stable, smooth solution to the Isoperimetric Problem in Gaussian space (2013, background): “ are also the only compact smooth hyper-surfaces which are local minimizers for the Isoperimetric Problem in Rn+1. Homotheties also play an important role in other work such as that of Morgan-Ritor´e [10], Palmer [12], and Wente [18]. 4 MATTHEW MCGONAGLE AND JOHN ROSS For the case of Σ ⊂ B2R(0) and ”
Some isoperimetric comparison theorems for convex bodies in Riemannian manifolds (2003, background): “In [ MR , Lemma 3.1] it was shown that the existence of {'"}">0 is guaranteed for a bounded, constant mean curvature hypersurface � with a closed singular set �0 = � − � such that Hn−2(�0) = 0 or consisting of isolated points.”