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内容説明 This book presents a new front of research in conformal geometry， on sign-changing Yamabe-type problems and contact form geometry in particular. New ground is broken with the establishment of a Morse lemma at infinity for sign-changing Yamabe-type problems. This family of problems， thought to be out of reach a few years ago， becomes a family of problems which can be studied: the book lays the foundation for a program of research in this direction. In contact form geometry， a cousin of symplectic geometry， the authors prove a fundamental result of compactness in a variational problem on Legrendrian curves， which allows one to define a homology associated to a contact structure and a vector field of its kernel on a three-dimensional manifold. The homology is invariant under deformation of the contact form， and can be read on a sub-Morse complex of the Morse complex of the variational problem built with the periodic orbits of the Reeb vector-field. This book introduces， therefore， a practical tool in the field， and this homology becomes computable.