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15
98
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Extending functions on boundary into M as a harmonic function

Published on
#harmonic-functions #manifolds-with-boundary #compact-manifolds
178
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Independence of definition of boundary point of a manifold

Published on
#differential-geometry #differential-forms #manifolds-with-boundary
859
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How is the "surface measure" on a manifold defined?

Published on
#real-analysis #measure-theory #manifolds #manifolds-with-boundary #submanifold
244
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Proof of that if $M$ is a $n$-manifold oriented, then $\partial M$ is a $(n-1)$-manifold oriented

Published on
#differential-geometry #proof-explanation #manifolds-with-boundary
620
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Existence of a unique "outer" normal vector

Published on
#differential-geometry #manifolds #smooth-manifolds #manifolds-with-boundary #submanifold
638
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When is a minimal geodesic a shortest path?

Published on
#differential-geometry #reference-request #metric-spaces #riemannian-geometry #manifolds-with-boundary
81
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Why the boundary of $M_1\# M_2$ is incompressible if the boundaries of $M_i$ are incompressible?

Published on
#algebraic-topology #manifolds #low-dimensional-topology #manifolds-with-boundary
174
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Boundaries of manifolds and algebraic topology

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#algebraic-topology #homology-cohomology #manifolds-with-boundary
62
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When both $U$ and $W$ are open in $\mathbb{H}^k$ and $\mathbb{H}^l$, respectively, then why $U\times W$ cannot be open in $\mathbb{H}^{k+l}$

Published on
#real-analysis #manifolds #smooth-manifolds #manifolds-with-boundary
237
Views

Boundary of a one-dimensional manifold - choosing an oriented atlas

Published on
#manifolds #smooth-manifolds #manifolds-with-boundary
63
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Understanding the definition of boundary points of a manifold

Published on
#manifolds-with-boundary
57
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Image of smooth map lies in interior

Published on
#differential-geometry #smooth-manifolds #manifolds-with-boundary
341
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Manifold with boundary and topological boundary

Published on
#manifolds #smooth-manifolds #manifolds-with-boundary
364
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Prove there exists a outward unit normal field on the boundary this manifold

Published on
#differential-geometry #orientation #manifolds-with-boundary
79
Views

Reference request Eigenspace decomposition Hodge Laplacian on forms on manifolds with boundary

Published on
#differential-forms #manifolds-with-boundary #hodge-theory #compact-manifolds

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