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Examples ofquasi-isometry
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Since anyquasi-isometrybetween negatively curved simply connected manifolds induces a quasiconformal map of the boundaries, we have the following.
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Indeed, the above statement is equivalent to subgraph closure together withquasi-isometryinvariance.
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From this, we may conclude easily that diabolicity isquasi-isometryinvariant among uniformly locally finite graphs.
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We illustrate the consequence ofquasi-isometryby the following theorems.
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Such a map 2 does not need to be either one-to-one or onto; however, it must be aquasi-isometry.
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Note that aquasi-isometryis not assumed to be continuous, for example any map between compact metric spaces is aquasiisometry.
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This example is from Wikipedia and may be reused under a CC BY-SA license.In advanced mathematics,quasi-isometrycan be used as a criterion to state that two shapes are approximately the same.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Note that aquasi-isometryis not required to be continuous.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Formally, this means classifying finitely generated groups with their word metric up toquasi-isometry.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Any property of metric spaces that only depends on a space'squasi-isometryclass immediately yields another invariant of groups, opening the field of group theory to geometric methods.
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Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.