# A convergence result for the Gradient Flow of ∫ |A| 2 in Riemannian Manifolds

Geometric Flows (2015)

- Volume: 1, Issue: 1, page 609-639
- ISSN: 2353-3382

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topAnnibale Magni. " A convergence result for the Gradient Flow of ∫ |A| 2 in Riemannian Manifolds ." Geometric Flows 1.1 (2015): 609-639. <http://eudml.org/doc/275889>.

@article{AnnibaleMagni2015,

abstract = {We study the gradient flow of the L2−norm of the second fundamental form for smooth immersions of two-dimensional surfaces into compact Riemannian manifolds. By analogy with the results obtained in [10] and [11] for the Willmore flow, we prove lifespan estimates in terms of the L2−concentration of the second fundamental form of the initial data and we show the existence of blowup limits. Under special condition both on the initial data and on the target manifold, we prove a long time existence result for the flow and the subconvergence to a critical immersion.},

author = {Annibale Magni},

journal = {Geometric Flows},

keywords = {Higher order geometric flows; Willmore functional; geometric measure theory; mean curvature flow; reduced Allen-Cahn action functional; action minimization problem; compactness; lower semicontinuity; Euler-Lagrange equation; symmetries},

language = {eng},

number = {1},

pages = {609-639},

title = { A convergence result for the Gradient Flow of ∫ |A| 2 in Riemannian Manifolds },

url = {http://eudml.org/doc/275889},

volume = {1},

year = {2015},

}

TY - JOUR

AU - Annibale Magni

TI - A convergence result for the Gradient Flow of ∫ |A| 2 in Riemannian Manifolds

JO - Geometric Flows

PY - 2015

VL - 1

IS - 1

SP - 609

EP - 639

AB - We study the gradient flow of the L2−norm of the second fundamental form for smooth immersions of two-dimensional surfaces into compact Riemannian manifolds. By analogy with the results obtained in [10] and [11] for the Willmore flow, we prove lifespan estimates in terms of the L2−concentration of the second fundamental form of the initial data and we show the existence of blowup limits. Under special condition both on the initial data and on the target manifold, we prove a long time existence result for the flow and the subconvergence to a critical immersion.

LA - eng

KW - Higher order geometric flows; Willmore functional; geometric measure theory; mean curvature flow; reduced Allen-Cahn action functional; action minimization problem; compactness; lower semicontinuity; Euler-Lagrange equation; symmetries

UR - http://eudml.org/doc/275889

ER -

## References

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