Skip to main content
MathOverflow

Return to Question

edited grammar and tex code
Source Link
Igor Belegradek
Igor Belegradek
  • 29.1k
  • 2
  • 80
  • 176

Let M$M$ be a Riemannian manifold, x$x$ and y$y$ are two pintspoints in M$M$. Assume that x$x$ is not in the cut locus of y, then whether$y$. Does there exist a neighborhood U$U$ of x$x$ and a neighborhood V$V$ of y$y$ such that for every point u$u$ in U$U$ and for every point v$v$ in V$V$ we have that u$u$ is not in the cut locus of v$v$?

Let M be a Riemannian manifold, x and y are two pints in M. Assume that x is not in the cut locus of y, then whether there exist a neighborhood U of x and a neighborhood V of y such that for every point u in U and for every point v in V we have that u is not in the cut locus of v?

Let $M$ be a Riemannian manifold, $x$ and $y$ are two points in $M$. Assume that $x$ is not in the cut locus of $y$. Does there exist a neighborhood $U$ of $x$ and a neighborhood $V$ of $y$ such that for every point $u$ in $U$ and for every point $v$ in $V$ we have that $u$ is not in the cut locus of $v$?

Source Link
ProbLe
ProbLe
  • 265
  • 2
  • 9

An elementary question about the cut locus

Let M be a Riemannian manifold, x and y are two pints in M. Assume that x is not in the cut locus of y, then whether there exist a neighborhood U of x and a neighborhood V of y such that for every point u in U and for every point v in V we have that u is not in the cut locus of v?