698 research outputs found
Ricci Flow under Kato-type curvature lower bound
In this work, we extend the existence theory of non-collapsed Ricci flows
from point-wise curvature lower bound to Kato-type lower bound. As an
application, we prove that compact three dimensional non-collapsed strong Kato
limit space is homeomorphic to a smooth manifold. We also use the Ricci flow
smoothing to study stability problem in scalar curvature geometry.Comment: reference updated, typos fixed, 20 page
Conformal tori with almost non-negative scalar curvature
In this work, we consider sequence of metrics with almost non-negative scalar
curvature on torus. We show that if the sequence is uniformly conformal to
another sequence of metrics with uniformly controlled geometry, then it
converges to a flat metric in the volume preserving intrinsic flat sense,
sense and the measured Gromov-Hausdorff sense.Comment: 20 page
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