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The Ambient Metric (AM-178)
This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics. The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation of the ambient obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally...
Geometric and Spectral Analysis
In 2012, the Centre de Recherches Mathématiques was at the center of many interesting developments in geometric and spectral analysis, with a thematic program on Geometric Analysis and Spectral Theory followed by a thematic year on Moduli Spaces, Extremality and Global Invariants. This volume contains original contributions as well as useful survey articles of recent developments by participants from three of the workshops organized during these programs: Geometry of Eigenvalues and Eigenfunctions, held from June 4-8, 2012; Manifolds of Metrics and Probabilistic Methods in Geometry and Analysis, held from July 2-6, 2012; and Spectral Invariants on Non-compact and Singular Spaces, held from July 23-27, 2012. The topics covered in this volume include Fourier integral operators, eigenfunctions, probability and analysis on singular spaces, complex geometry, Kähler-Einstein metrics, analytic torsion, and Strichartz estimates. This book is co-published with the Centre de Recherches Mathématiques.
Clinical Practice Guidelines We Can Trust
Advances in medical, biomedical and health services research have reduced the level of uncertainty in clinical practice. Clinical practice guidelines (CPGs) complement this progress by establishing standards of care backed by strong scientific evidence. CPGs are statements that include recommendations intended to optimize patient care. These statements are informed by a systematic review of evidence and an assessment of the benefits and costs of alternative care options. Clinical Practice Guidelines We Can Trust examines the current state of clinical practice guidelines and how they can be improved to enhance healthcare quality and patient outcomes. Clinical practice guidelines now are ubiqu...
Partial Differential Equations and Complex Analysis
Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has been a significant interaction between the theory of partial differential equations and the function theory of several complex variables. Partial Differential Equations and Complex Analysis explores the background and plumbs the depths of this symbiosis. The book is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the ?-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.
Complex Geometry
Presents the proceedings of an international conference on complex geometry and related topics, held in commemoration of the 50th anniversary of Osaka University, Osaka, Japan. The text focuses on the CR invariants, hyperbolic geometry, Yamabe-type problems, and harmonic maps.
Complex Analysis II
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Complex Analysis I
The past several years have witnessed a striking number of important developments in Complex Analysis. One of the characteristics of these developments has been to bridge the gap existing between the theory of functions of one and of several complex variables. The Special Year in Complex Analysis at the University of Maryland, and these proceedings, were conceived as a forum where these new developments could be presented and where specialists in different areas of complex analysis could exchange ideas. These proceedings contain both surveys of different subjects covered during the year as well as many new results and insights. The manuscripts are accessible not only to specialists but to a broader audience. Among the subjects touched upon are Nevanlinna theory in one and several variables, interpolation problems in Cn, estimations and integral representations of the solutions of the Cauchy-Riemann equations, the complex Monge-Ampère equation, geometric problems in complex analysis in Cn, applications of complex analysis to harmonic analysis, partial differential equations.
Metalloids in Biology
Metalloids belong to class of elements that exhibit physiochemical characteristics intermediating between those of metals and non-metals. Some are quasi-essential for the overall growth and development of plants. Silicon, for instance, enhances plant structural integrity, while boron is crucial for cell wall formation, and selenium acts as an antioxidant but some are toxic, like germanium (Ge) and arsenic (As), as they threaten the soil ecosystem and human health. Metalloid toxicity hinges on their cellular concentrations ,where low levels aid plant development ,whereas high levels cause harmful effects. Thus, it is crucial to encompass the underlying detoxification mechanisms behind metallo...
