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A $k+1$ Manifold whose boundary is the solution set to the equation $f(\vec{x})=\vec{0}$

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#real-analysis #multivariable-calculus #manifolds #manifolds-with-boundary
98
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Show that a given set is a manifold with boundary

Published on
#manifolds #manifolds-with-boundary
255
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Lenght of the curve in Riemannian metric.

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#manifolds #riemannian-geometry #manifolds-with-boundary #arc-length
523
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Induced orientation on manifold

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#differential-geometry #differential-topology #orientation #manifolds-with-boundary
80
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How to define an atlas on this manifold with boundary?

Published on
#manifolds #manifolds-with-boundary
93
Views

Integration over manifold

Published on
#differential-geometry #manifolds-with-boundary #stokes-theorem
93
Views

Is $\overline{u^{-1}((-\infty,a))}$ a $C^k$-manifold with boundary for a $C^k$ function $u$?

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#differential-geometry #manifolds #differential-topology #geometric-topology #manifolds-with-boundary
102
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Topological boundary as a submanifold

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#differential-geometry #manifolds #manifolds-with-boundary
289
Views

$\sin(\frac{1}{x})$ on $\Bbb R^2$ interior, cluster points, boundary

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#real-analysis #general-topology #manifolds-with-boundary
200
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Is the hemisphere of $S^4$ the unique compact 4-dimensional manifold with $\partial K = S^3$?

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#differential-geometry #algebraic-topology #compact-manifolds #manifolds-with-boundary #orbifolds
1.1k
Views

On the trace theory and restrictions of Sobolev space functions

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#real-analysis #partial-differential-equations #sobolev-spaces #boundary-value-problem #manifolds-with-boundary
188
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Topological boundary of a specific manifold.

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#differential-geometry #proof-verification #manifolds #differential-topology #manifolds-with-boundary
813
Views

An orientation on a $(n-1)$-dimensional submanifold.

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#differential-geometry #manifolds #differential-topology #orientation #manifolds-with-boundary
379
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Can every Riemmanian Manifold be completed?

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#differential-geometry #manifolds #differential-topology #riemannian-geometry #manifolds-with-boundary
417
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Compact 3-manifolds with boundary an orientable surface

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#algebraic-topology #geometric-topology #low-dimensional-topology #manifolds-with-boundary

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