30 May 2016

EIGENVALUE ESTIMATE FOR THE BASIC LAPLACIAN ON MANIFOLDS WITH FOLIATED BOUNDARY | MATH SEMINAR

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Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary, a Math seminar which was organized by the Department of Mathematics and Statistics - Faculty of Natural and Applied Sciences at NDU, Main Campus, on May 30, in a joint work with Fida El Chami, Georges Habib and Roger Nakad, derived a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic 1-forms defined on a compact manifold whose boundary is endowed with a Riemannian flow.

The limiting case gives rise to a particular geometry of the flow and the boundary. Namely, the flow is a local product and the boundary is η-umbilical. This allows to characterize the quotient of R ᵡ B (B denotes the unit closed ball) by some group Γ as being the limiting manifold. Finally, several rigidity results describing the product S¹ ᵡ Sⁿ  were deduced as the boundary of some manifold.

The Speaker at the seminar was Dr. Ola Makhoul (Lebanese University).

  • Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary | Math Seminar 2016 1
  • Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary | Math Seminar 2016 2
  • Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary | Math Seminar 2016 3
  • Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary | Math Seminar 2016 4
  • Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary | Math Seminar 2016 5
  • Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary | Math Seminar 2016 6
  • Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary | Math Seminar 2016 7
  • Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary | Math Seminar 2016 1
  • Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary | Math Seminar 2016 2
  • Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary | Math Seminar 2016 3
  • Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary | Math Seminar 2016 4
  • Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary | Math Seminar 2016 5
  • Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary | Math Seminar 2016 6
  • Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary | Math Seminar 2016 7

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