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Are minimal area and mean curvature definitions of minimal surfaces really equivalent?

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#analysis #differential-geometry #surfaces #geodesic #minimal-surfaces
475
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How to calculate the mean curvature of clifford torus immersed in the standard sphere $\mathbb{S}^3$?

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#differential-geometry #minimal-surfaces
88
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Why $\langle x_i,x_{jk}\rangle=0$ holds true?

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#differential-geometry #minimal-surfaces
101
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Does any compact boundary become a minimal hypersurface iff each of the boundary component is a minimal hypersurface?

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#general-topology #differential-geometry #riemannian-geometry #curvature #minimal-surfaces
233
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Is the surface $z=\ln \cos x-\ln \cos y$ minimal?

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#differential-geometry #minimal-surfaces
75
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Lemma 1.19 in Colding-Minicozzi

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#differential-geometry #partial-differential-equations #minimal-surfaces
43
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Is any minimal hypersurface also a minimal submanifold?

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#differential-geometry #riemannian-geometry #curvature #submanifold #minimal-surfaces
38
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Lemma 1.34 in Colding-Minicozzi

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#partial-differential-equations #riemannian-geometry #elliptic-equations #minimal-surfaces
90
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Why is the minimal surface of revolution not a cylinder?

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#area #surfaces #calculus-of-variations #minimal-surfaces
48
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Minimal surfaces, but 1 dimension lower

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#geometry #differential-geometry #euclidean-geometry #minimal-surfaces
31
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Verifying a Scaled Variable Function Satisfies the Minimal Surface Equation

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#partial-differential-equations #minimal-surfaces
27
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Marginally Outer Trapped Surface as a Minimal Surface

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#general-relativity #minimal-surfaces
47
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The distribution of normal vectors of minimal surfaces

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#geometry #differential-geometry #minimal-surfaces
74
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On Schoen and Yau's proof of the positive mass theorem: extracting a minimal surface in the limit

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#riemannian-geometry #uniform-convergence #mathematical-physics #minimal-surfaces #arzela-ascoli
46
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What does it mean that the helicoid can 'glide' over itself?

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#general-topology #geometry #surfaces #minimal-surfaces

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