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A comparison theorem for the Levi equation

Giovanna Citti (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We prove a strong comparison principle for the solution of the Levi equation L ( u ) = i = 1 n ( ( 1 + u t 2 ) ( u x i x i + u y i y i ) + ( u x i 2 + u y i 2 ) u t t + 2 ( u y i - u x i u t ) u x i t - 2 ( u x i + u y i u t ) u y i t + k ( x , y , t ) ( 1 + | D u | 2 ) 3 / 2 = 0 , applying Bony Propagation Principle.

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

Annibale Magni (2015)

Geometric Flows

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...

A Hörmander-type spectral multiplier theorem for operators without heat kernel

Sönke Blunck (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Hörmander’s famous Fourier multiplier theorem ensures the L p -boundedness of F ( - Δ D ) whenever F ( s ) for some s > D 2 , where we denote by ( s ) the set of functions satisfying the Hörmander condition for s derivatives. Spectral multiplier theorems are extensions of this result to more general operators A 0 and yield the L p -boundedness of F ( A ) provided F ( s ) for some s sufficiently large. The harmonic oscillator A = - Δ + x 2 shows that in general s > D 2 is not sufficient even if A has a heat kernel satisfying gaussian estimates. In this paper,...

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