Displaying similar documents to “The third Betti number of a positively pinched riemannian six manifold”

Harnack inequalities on a manifold with positive or negative Ricci curvature.

Dominique Bakry, Zhongmin M. Qian (1999)

Revista Matemática Iberoamericana

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Several new Harnack estimates for positive solutions of the heat equation on a complete Riemannian manifold with Ricci curvature bounded below by a positive (or a negative) constant are established. These estimates are sharp both for small time, for large time and for large distance, and lead to new estimates for the heat kernel of a manifold with Ricci curvature bounded below.

Cramér's formula for Heisenberg manifolds

Mahta Khosravi, John A. Toth (2005)

Annales de l'institut Fourier

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Let R ( λ ) be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that ∫ 1 T | R ( t ) | 2 d t = c T 5 2 + O δ ( T 9 4 + δ ) , where c is a specific nonzero constant and δ is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that R ( t ) = O δ ( t 3 4 + δ ) .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the 2 n + 1 -dimensional case. ...

An inverse problem for the equation ▵ u = - c u - d

Michael Vogelius (1994)

Annales de l'institut Fourier

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Let Ω be a bounded, convex planar domain whose boundary has a not too degenerate curvature. In this paper we provide partial answers to an identification question associated with the boundary value problem ▵ u = - c u - d in Ω , u = 0 on ∂ Ω . We prove two results: 1) If Ω is not a ball and if one considers only solutions with - c u - d ≤ 0 , then there exist at most finitely many pairs of coefficients ( c , d ) so that the normal derivative ∂ u ∂ ν | ∂ Ω equals a given ψ ≠ 0 . 2) If one imposes no sign condition on the...

Short-time heat flow and functions of bounded variation in R N

Michele Miranda, Diego Pallara, Fabio Paronetto, Marc Preunkert (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove a characterisation of sets with finite perimeter and B V functions in terms of the short time behaviour of the heat semigroup in R N . For sets with smooth boundary a more precise result is shown.