query: Show that an expansion map is an isometry
positive_passages.docid: 152493
positive_passages.text: Is an expanding map on a compact metric space continuous?
negative_passages.docid: 95058
negative_passages.text: Finding a conformal map of slit disk on to unit disk
negative_passages.docid: 45276
negative_passages.text: Continuous map on $S^2$
negative_passages.docid: 152927
negative_passages.text: seemingly nontrivial question about covering maps and evenly covered open sets
negative_passages.docid: 119247
negative_passages.text: Let $(M,d)$ be a compact metric space and $f:M \to M$ such that $d(f(x),f(y)) \ge d(x,y) , \forall x,y \in M$ , then $f$ is isometry?
negative_passages.docid: 41617
negative_passages.text: If a $C^1$ map $f:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ is expanding ($\|f(x)-f(y)\|\geq\|x-y\|$), which of these must be true?
negative_passages.docid: 58000
negative_passages.text: How can one show that a möbius transformation maps the unit circle to some axis?
negative_passages.docid: 39763
negative_passages.text: Proving left-invariance (and proof-verification for right-invariance) for metric constructed from left-invariant Haar measure
negative_passages.docid: 71975
negative_passages.text: Showing that an Isometry on the Euclidean Plane fixing the origin is Linear
negative_passages.docid: 54222
negative_passages.text: Prove the map has a fixed point
negative_passages.docid: 109643
negative_passages.text: Prove that every isometry on $\mathbb{R}^2$ is bijective
negative_passages.docid: 118049
negative_passages.text: Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
negative_passages.docid: 95250
negative_passages.text: Proof a special extension on the isoperimetric theorem
negative_passages.docid: 91322
negative_passages.text: A diffeomorphism whose tangent map preserves dot products is an isometry.
negative_passages.docid: 146839
negative_passages.text: Orthogonal Projection onto the $ {L}_{\infty} $ Unit Ball
negative_passages.docid: 1932
negative_passages.text: How to show this equality of $\rho(X,Y)$
negative_passages.docid: 107321
negative_passages.text: How to show convexity of a ball in metric space?