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Sam
Sam
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Say in $R^3$, is there a sequence of smooth graphs $f_n$ over some plane P, such that the graphs as submanifolds in $R^3$ converge in the sense of varifold (as Radon measures on $R^3 \times Gr(2,3)$ ) to a limit V, which is multiplicity 2 of the plane P? Seems impossible but is there a proof?

Say in $R^3$, is there a sequence of graphs $f_n$ over some plane P, such that the graphs as submanifolds in $R^3$ converge in the sense of varifold (as Radon measures on $R^3 \times Gr(2,3)$ ) to a limit V, which is multiplicity 2 of the plane P? Seems impossible but is there a proof?

Say in $R^3$, is there a sequence of smooth graphs $f_n$ over some plane P, such that the graphs as submanifolds in $R^3$ converge in the sense of varifold (as Radon measures on $R^3 \times Gr(2,3)$ ) to a limit V, which is multiplicity 2 of the plane P? Seems impossible but is there a proof?

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Sam
Sam
  • 49
  • 3

sequence of graphs converge in the sense of varifold to multiplicity 2 plane

Say in $R^3$, is there a sequence of graphs $f_n$ over some plane P, such that the graphs as submanifolds in $R^3$ converge in the sense of varifold (as Radon measures on $R^3 \times Gr(2,3)$ ) to a limit V, which is multiplicity 2 of the plane P? Seems impossible but is there a proof?