Lefschetz fixed point formula on a compact Riemannian manifold with boundary for some boundary conditions

Struwe’s decomposition for a Polyharmonic operator on a compact Riemannian manifold with or without boundary

Boundary conditions in supergravity on a manifold with boundary

We explain why it is necessary to use boundary conditions in the proof of supersymmetry of a supergravity action on a manifold with boundary. Working in both boundary (“downstairs”) and orbifold (“upstairs”) pictures, we present a bulkplus-boundary/brane action for the five-dimensional (on-shell) supergravity which is supersymmetric with the use of fewer boundary conditions than were previously...

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

Gradient estimates for eigenfunctions on compact Riemannian manifolds with boundary

The purpose of this paper is to prove the L∞ gradient estimates and L∞ gradient estimates for the unit spectral projection operators of the Dirichlet Laplacian and Neumann (or more general, Ψ1-Robin) Laplacian on compact Riemannian manifolds (M, g) of dimension n ≥ 2 with C2 boundary . And we also get an upper bounds for normal derivatives of the unit spectral projection operators of the Dirich...

Lefschetz Fixed Point Formula for Manifolds with Cylindrical Ends