The moduli space of two-convex embedded spheres

Reto Buzano; Robert Haslhofer; Or Hershkovits

doi:10.4310/jdg/1622743139

The moduli space of two-convex embedded spheres

Reto Buzano, Robert Haslhofer, Or Hershkovits

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that the moduli space of 2-convex embedded n-spheres in Rⁿ⁺¹ is path-connected for every n. Our proof uses mean curvature flow with surgery and can be seen as an extrinsic analog to Marques’ influential proof of the path-connectedness of the moduli space of positive scalar curvature metrics on three-manifolds [21].

Original language	English
Pages (from-to)	189-221
Number of pages	33
Journal	Journal of Differential Geometry
Volume	118
Issue number	2
DOIs	https://doi.org/10.4310/jdg/1622743139
State	Published - Jun 2021
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Geometry and Topology

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title = "The moduli space of two-convex embedded spheres",

abstract = "We prove that the moduli space of 2-convex embedded n-spheres in Rn+1 is path-connected for every n. Our proof uses mean curvature flow with surgery and can be seen as an extrinsic analog to Marques{\textquoteright} influential proof of the path-connectedness of the moduli space of positive scalar curvature metrics on three-manifolds [21].",

author = "Reto Buzano and Robert Haslhofer and Or Hershkovits",

year = "2021",

month = jun,

doi = "10.4310/jdg/1622743139",

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AU - Haslhofer, Robert

AU - Hershkovits, Or

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AB - We prove that the moduli space of 2-convex embedded n-spheres in Rn+1 is path-connected for every n. Our proof uses mean curvature flow with surgery and can be seen as an extrinsic analog to Marques’ influential proof of the path-connectedness of the moduli space of positive scalar curvature metrics on three-manifolds [21].

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U2 - 10.4310/jdg/1622743139

DO - 10.4310/jdg/1622743139

M3 - مقالة

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VL - 118

SP - 189

EP - 221

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

IS - 2

ER -

The moduli space of two-convex embedded spheres

Abstract

All Science Journal Classification (ASJC) codes

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