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15
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Rank of mapping betweeen two manifolds

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#manifolds #differential-topology #matrix-rank #manifolds-with-boundary
40
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Is there an example of reducible compact 3-manifold with boundary that has no embedded incompressible two-sided surface?

Published on
#manifolds #geometric-topology #low-dimensional-topology #manifolds-with-boundary #compact-manifolds
598
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Stokes' Theorem general case

Published on
#real-analysis #general-topology #stokes-theorem #manifolds-with-boundary #divergence-theorem
297
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Fréchet manifold structure on space of sections

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#differential-geometry #manifolds #fiber-bundles #manifolds-with-boundary #global-analysis
243
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Definition of a submanifold with boundary

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#differential-geometry #manifolds-with-boundary #submanifold
81
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Show that these two diffeomorphisms cannot exist simultaneously

Published on
#differential-geometry #manifolds-with-boundary #diffeomorphism #submanifold
368
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When is a chart of a submanifold not only a homeomorphism, but a diffeomorphism?

Published on
#differential-geometry #smooth-manifolds #manifolds-with-boundary #submanifold
74
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Unsound definition of interior and boundary points of a submanifold of $\mathbb R^N$

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#differential-geometry #manifolds-with-boundary #submanifold
289
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Characterization of the tangent space of the boundary of an embedded submanifold of $\mathbb R^d$ with boundary

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#differential-geometry #smooth-manifolds #manifolds-with-boundary #tangent-spaces #submanifold
175
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Construct interior chart of a manifold boundary $\partial M$ from a boundary chart of the manifold $M$

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#differential-geometry #manifolds #smooth-manifolds #manifolds-with-boundary #submanifold
102
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Show an identity for the Laplace-Beltrami operator

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#differential-geometry #smooth-manifolds #laplacian #manifolds-with-boundary #tangent-spaces
547
Views

Why is it important the manifold has codimension $1$ in order to prove this identity for $\operatorname{div}fV$ on $\partial M$?

Published on
#differential-geometry #surfaces #manifolds-with-boundary #tangent-spaces #submanifold
115
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Show this identity for the surface measure on the boundary of a submanifold

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#differential-geometry #smooth-manifolds #geometric-measure-theory #manifolds-with-boundary #submanifold
218
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Find a specific countable atlas for a smooth submanifold with boundary

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#differential-geometry #smooth-manifolds #manifolds-with-boundary #submanifold
64
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A chart of a $k$-dimensional submanifold maps interior points to $(\mathbb H^k)^\circ$ and boundary points to $\partial\mathbb H^k$

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#differential-geometry #smooth-manifolds #manifolds-with-boundary #diffeomorphism #submanifold

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