# 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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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 23 REFERENCES

## On the spectral geometry of algebraic curves

J. Brüning, M. Lesch
• J. reine angew. Math. 474
• 1996
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

## Spectral geometry of singular Riemannian spaces

VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

## On the Hodge theory of Riemannian pseudomanifolds

VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

## An index theorem for manifolds with metric horns

M. Lesch, N. Peyerimhoff
• Comm. Partial Differential Equations 23
• 1998
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

## The signature theorem for manifolds with metric horns

VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

## On the existence of small-time heat expansions for operators with irregular singularities in the coefficients

VIEW 2 EXCERPTS
HIGHLY INFLUENTIAL

## Resolution of Singularities and Division of Distributions

VIEW 1 EXCERPT
HIGHLY INFLUENTIAL

VIEW 1 EXCERPT

## Local bi-Lipschitz classification of 2-dimensional semialgebraic sets

L. Birbrair
• Houston J. Math. 25
• 1999
VIEW 1 EXCERPT

VIEW 1 EXCERPT