A Course in Minimal Surfaces

By T. Colding, W. Minicozzi. 2011

408 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1763648cacd494af0edc63058d7e800375d1731f

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In Applied Mathematics

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Stability and compactness for complete f -minimal surfaces (2012, methodology): “o isometric immersions of Σ: (Σ,g) → (M,g) and (Σ,˜g) → (M,˜g) respectively. When (Σ,˜g) is minimal, it is well known that the second variation of the volume of (Σ,g˜) is given by Proposition 12. (cf [6]) Let (Σ,˜g) be minimal submanifold in (M,˜g). If T is a normal compactly supported variational v”
Comparing the Morse index and the first Betti number of minimal hypersurfaces (2016, background): “e tangent bundle of Nn+1. In fact, Q(W,W) gives precisely the second variation of the volume of Mn at t = 0 under a ﬂow φt generated by any vector ﬁeld X ∈ X(N) that coincides with W on Mn (see e. g. [10]). The index of a closed embedded minimal hypersurface Mn of Nn+1 is the maximal dimension of a ”
Translating graphs by mean curvature flow (2012, methodology): “ll with radius s and center x. Similarly, For x ∈ Σ, BΣ s (x) ⊂ Σ denotes the intrinsic geodesic ball and r the intrinsic distance to x. Theorem 3.1 (Schoen Curvature estimate [15], Colding-Minicozzi [4]). If Σ2 ⊂ M3 is an immersed stable minimal surface with trivial normal bundle and Br 0 = BΣ r0 (”
Sharp eigenvalue bounds and minimal surfaces in the ball (2012, background): “s a ﬁxed geodesic distance from ∂Σk. Since the area is also bounded we have a sequence k′ such that Σk′ converges in C3 norm to a smooth minimal surface Σ∞ possibly with multiplicity (see for example [CM], Proposition 7.14 and its proof). We show that Σ∞ is a disk containing the origin and the multi”
Min-max for phase transitions and the existence of embedded minimal hypersurfaces (2015, methodology): “ OF EMBEDDED MINIMAL HYPERSURFACES 37 In a neighborhood of xwe can assume that K M, the sectional curvature of M, is bounded by k. An application of the Hessian comparison theorem (see Lemma 7.1 from [5]) gives (16) p 2 (Hessr)(X;X) 1 r jX (Xrr)rrj k for jXj= 1 and rsmall enough. Plugging ginto equ”