arXiv subjects

Karen Corrales

Publications and source records attributed to Karen Corrales.

3 recordsLinked to original sources

arXiv2021

On the ADM mass of Kähler scalar flat ALE metrics

In this paper we study the behaviour of scalar flat Kähler ALE spaces and their ADM mass under blow ups. In particular we prove that by blowing up sufficiently many points at sufficiently big mutual distance one can produce scalar flat metrics with arbitrarily large ADM mass. A general machinery for producing scalar flat non Ricci flat ALE spaces of zero ADM mass is also presented, using and integrating previous work by Rollin-Singer and Hein-LeBrun.

math.DG↗

arXiv2018

Existence of CMC-foliations in asymptotically cuspidal manifolds

In this paper we prove existence and uniqueness of a CMC foliation in asymptotically cuspidal manifolds. Moreover, we study the isoperimetric problem in this case. Our proof does not require any curvature assumption and it holds for any dimension.

math.DG↗

arXiv2016

Non existence of Type II singularities for embedded and unknotted space curves

In this paper we prove that a certain class of embedded unknotted curves in $\mathbb{R}^3$ evolving under curve shortening flow do not form singularities Type II before collapsing to a point. Our proof uses tools of the minimal surface theory to study a suitable isoperimetric ratio.

math.DG↗