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YCor
YCor
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Neil Hoffman
Neil Hoffman
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I know that generally the geodesic distance $d_x$ from a point $x$ in a Finsler space is not smooth ($C^\infty$). According to Shen, the square of it is just $C^1$ at $x$. Now I am woderingwondering if there exists any number $n$ that makes $(d_x)^n$ smooth in $x$?

I know that generally the geodesic distance $d_x$ from a point $x$ in a Finsler space is not smooth ($C^\infty$). According to Shen, the square of it is just $C^1$ at $x$. Now I am wodering if there exists any number $n$ that makes $(d_x)^n$ smooth in $x$?

I know that generally the geodesic distance $d_x$ from a point $x$ in a Finsler space is not smooth ($C^\infty$). According to Shen, the square of it is just $C^1$ at $x$. Now I am wondering if there exists any number $n$ that makes $(d_x)^n$ smooth in $x$?

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Majid
Majid
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Smoothness of some power of the geodesic distance in a Finsler geometry

I know that generally the geodesic distance $d_x$ from a point $x$ in a Finsler space is not smooth ($C^\infty$). According to Shen, the square of it is just $C^1$ at $x$. Now I am wodering if there exists any number $n$ that makes $(d_x)^n$ smooth in $x$?