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A Fixed Point Theorem for Holomorphic Mappings
Variation Integrals in Fiber Bundles
Note on the Differentiability of Nonlinear Semigroups
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adjoint algebra analytic assume Assumptions asymptotic Banach space boundary conditions boundary value problems bounded sets Cauchy closed subspace coefficients coercive cohomology commutes consider constant continuous mapping converges strongly converges weakly coordinate corresponding critical points defined deformation denote diffeomorphism dimension Dirichlet form divergence form domain eigenfunctions eigenvalue eigenvalue problems element elliptic complex elliptic differential operator elliptic operators exact exterior fiber finite dimensional Finsler fixed point follows formula given Hence hermitian holomorphic hypothesis implies inequality infinite invariant isomorphism Laplace operator Lemma Let G line bundle Lusternik-Schnirelman Math Mc(f monotone morphism Neumann problem norm obtain operator of order partial differential equations Proof of Theorem prove pseudodifferential operator pseudolocal restriction Riemannian manifold Riemannian metric RMC structure satisfies Condition sections sequence smooth Sobolev solution subbundle submanifold Suppose symbol tangent bundle theory topological unique variational boundary vector bundle vector field Wmp(G zero