Corpus ID: 222141001

A characterization of non-collapsed $RCD(K, N)$ spaces via Einstein tensors

  title={A characterization of non-collapsed \$RCD(K, N)\$ spaces via Einstein tensors},
  author={Shouhei Honda and Xingyu Zhu},
  journal={arXiv: Differential Geometry},
We investigate the second principal term in the expansion of metrics $c(n)t^{(n+2)/2}g_t$ induced by heat kernel embedding into $L^2$ on a compact $RCD(K, N)$ space. We prove that the divergence free property of this term in the weak, asymptotic sense if and only if the space is non-collapsed up to multiplying a constant to the reference measure. This seems new even for weighted Riemannian manifolds. 
2 Citations
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  • B. Han
  • Mathematics, Physics
  • 2014
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