Let be a metric on the which is close to the standard metric , i.e. for some small, where is the norm with respect to (say). Is there an easy way of showing that the volume forms are close? Or even ?

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- Sep 28th 2013, 05:45 AMmarkwolfson16900Metrics close implies volume forms close
Let be a metric on the which is close to the standard metric , i.e. for some small, where is the norm with respect to (say). Is there an easy way of showing that the volume forms are close? Or even ?

- Jan 5th 2015, 02:20 AMRebesquesRe: Metrics close implies volume forms close
The Bishop-Gromov comparison theorem pops into mind.