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

100%

Magni A.

Geometric Flows

2015

tom 1

nr 1

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.

Cauchy problem for a class of parabolic systems of Shilov type with variable coefficients

84%

Litovchenko V., Dovzhytska I.

Open Mathematics

2012

tom 10

nr 3

1084-1102

In the case of initial data belonging to a wide class of functions including distributions of Gelfand-Shilov type we establish the correct solvability of the Cauchy problem for a new class of Shilov parabolic systems of equations with partial derivatives with bounded smooth variable lower coefficients and nonnegative genus. We also investigate the conditions of local improvement of the convergence of a solution of this problem to its limiting value when the time variable tends to zero.

Ograniczanie wyników

1 Geometric Flows

1 Open Mathematics

1 Dovzhytska I.

1 Litovchenko V.

1 Magni A.

1 2015

1 2012

Wyniki wyszukiwania

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

Cauchy problem for a class of parabolic systems of Shilov type with variable coefficients