The modified horizontal derivative and some of its applications (Q1921811)
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scientific article; zbMATH DE number 923530
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The modified horizontal derivative and some of its applications |
scientific article; zbMATH DE number 923530 |
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The modified horizontal derivative and some of its applications (English)
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3 September 1996
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The author studies the following theorem of Mukhometov. A simple metric \(g\) on a compact manifold with boundary is uniquely determined in its conformal class by distances among boundary points. Here \(g\) is called `simple' if any two points are joined by a unique geodesic. The author obtains a new estimate of stability and a kinematic formula for the volume of \(g\) which is linear in distances among boundary points. The new notion of modified horizontal derivative allows the author to obtain a variety of Mukhometov-type identities.
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kinematic formulae
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conformal class
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modified horizontal derivative
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