Local Geometry of Singular Real Analytic Surfaces

@inproceedings{Grieser1999LocalGO,
  title={Local Geometry of Singular Real Analytic Surfaces},
  author={Daniel Grieser},
  year={1999}
}
Let V be a compact real analytic surface with isolated singularities embedded in $R^N$, and assume its smooth part is equipped with a Riemannian metric that is induced from some analytic Riemannian metric on $R^N$. We prove: 1. Each point of V has a neighborhood which is quasi-isometric (naturally and 'almost isometrically') to a union of metric cones and horns, glued at their tips. 2. A full asymptotic expansion, for any $p\in V$, of the length of $V\cap\{q:\dist(q,p)=r\}$ as r tends to zero… CONTINUE READING

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