TY - JOUR
T1 - Local Well-Posedness of Skew Mean Curvature Flow for Small Data in d≥ 4 Dimensions
AU - Huang, Jiaxi
AU - Tataru, Daniel
N1 - Publisher Copyright:
© 2022, The Author(s).
PY - 2022/2
Y1 - 2022/2
N2 - The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in Rd+2 (or more generally, in a Riemannian manifold). It can be viewed as a Schrödinger analogue of the mean curvature flow, or alternatively as a quasilinear version of the Schrödinger Map equation. In this article, we prove small data local well-posedness in low-regularity Sobolev spaces for the skew mean curvature flow in dimension d≥ 4.
AB - The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in Rd+2 (or more generally, in a Riemannian manifold). It can be viewed as a Schrödinger analogue of the mean curvature flow, or alternatively as a quasilinear version of the Schrödinger Map equation. In this article, we prove small data local well-posedness in low-regularity Sobolev spaces for the skew mean curvature flow in dimension d≥ 4.
UR - http://www.scopus.com/inward/record.url?scp=85123063206&partnerID=8YFLogxK
U2 - 10.1007/s00220-021-04303-8
DO - 10.1007/s00220-021-04303-8
M3 - Article
AN - SCOPUS:85123063206
SN - 0010-3616
VL - 389
SP - 1569
EP - 1645
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 3
ER -