Alberto G Setti's Books

Yamabe-type Equations on Complete, Noncompact Manifolds

By: Paolo Mastrolia,Marco Rigoli,Alberto G Setti

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Yamabe-type Equations on Complete, Noncompact Manifolds

By: Paolo Mastrolia,Marco Rigoli,Alberto G Setti

The aim of this monograph is to present a self-contained introduction to some geometric and analytic aspects of the Yamabe problem. The book also describes a wide range of methods and techniques that can be successfully applied to nonlinear differential equations in particularly challenging situations. Such situations occur where the lack of compactness, symmetry and homogeneity prevents the use of more standard tools typically used in compact situations or for the Euclidean setting. The work is written in an easy style that makes it accessible even to non-specialists. After a self-contained treatment of the geometric tools used in the book, readers are introduced to the main subject by means of a concise but clear study of some aspects of the Yamabe problem on compact manifolds. This study provides the motivation and geometrical feeling for the subsequent part of the work. In the main body of the book, it is shown how the geometry and the analysis of nonlinear partial differential equations blend together to give up-to-date results on existence, nonexistence, uniqueness and a priori estimates for solutions of general Yamabe-type equations and inequalities on complete, non-compact Riemannian manifolds.

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Page Count

261

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3034803761

ISBN 13

9783034803762

Vanishing and Finiteness Results in Geometric Analysis

A Generalization of the Bochner Technique

By: Stefano Pigola,Marco Rigoli,Alberto G Setti

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Vanishing and Finiteness Results in Geometric Analysis

A Generalization of the Bochner Technique

By: Stefano Pigola,Marco Rigoli,Alberto G Setti

This book describes very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods, from spectral theory and qualitative properties of solutions of PDEs, to comparison theorems in Riemannian geometry and potential theory.

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Page Count

294

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764386428

ISBN 13

9783764386429

The Beilinson Complex and Canonical Rings of Irregular Surfaces

By: Alberto Canonaco

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The Beilinson Complex and Canonical Rings of Irregular Surfaces

By: Alberto Canonaco

An important theorem by Beilinson describes the bounded derived category of coherent sheaves on $\mathbb{P n$, yielding in particular a resolution of every coherent sheaf on $\mathbb{P n$ in terms of the vector bundles $\Omega {\mathbb{P n j(j)$ for $0\le j\le n$. This theorem is here extended to weighted projective spaces. To this purpose we consider, instead of the usual category of coherent sheaves on $\mathbb{P ({\rm w )$ (the weighted projective space of weights $\rm w=({\rm w 0,\dots,{\rm w n)$), a suitable category of graded coherent sheaves (the two categories are equivalent if and only if ${\rm w 0=\cdots={\rm w n=1$, i.e. $\mathbb{P ({\rm w )= \mathbb{P n$), obtained by endowing $\mathbb{P ({\rm w )$ with a natural graded structure sheaf. The resulting graded ringed space $\overline{\mathbb{P ({\rm w )$ is an example of graded scheme (in chapter 1 graded schemes are defined and studied in some greater generality than is needed in the rest of the work). Then in chapter 2 we prove This weighted version of Beilinson's theorem is then applied in chapter 3 to prove a structure theorem for good birational weighted canonical projections of surfaces of general type (i.e., for morphisms, which are birational onto the image, from a minimal surface of general type $S$ into a $3$-dimensional $\mathbb{P ({\rm w )$, induced by $4$ sections $\sigma i\in H0(S,\mathcal{O S({\rm w iK S))$). This is a generalization of a theorem by Catanese and Schreyer (who treated the case of projections into $\mathbb{P 3$), and is mainly interesting for irregular surfaces, since in the regular case a similar but simpler result (due to Catanese) was already known. The theorem essentially states that giving a good birational weighted canonical projection is equivalent to giving a symmetric morphism of (graded) vector bundles on $\overline{\mathbb{P ({\rm w )$, satisfying some suitable conditions. Such a morphism is then explicitly determined in chapter 4 for a family of surfaces with numerical invariant

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Page Count

114

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821841939

ISBN 13

9780821841938

The Legacy of Leon Van Hove

By: Alberto Giovannini

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The Legacy of Leon Van Hove

By: Alberto Giovannini

This important volume describes the wide-ranging scientific activities of Léon Van Hove, through commentaries by his colleagues and a selection of his most influential papers and documents. The reprinted papers are grouped by topic, starting from his early work in mathematics and theoretical and statistical physics, up to his very last contributions in elementary particle physics and multiparticle dynamics. Van Hove's career as teacher, director and science advisor in many European institutions is presented in sketches by friends and coworkers. A selection of his speeches and documented thoughts on science completes the volume.

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Page Count

596

Publisher

World Scientific

Published Date

ISBN 10

9812792724

ISBN 13

9789812792723

Maximum Principles on Riemannian Manifolds and Applications

By: Stefano Pigola,Marco Rigoli,Alberto Giulio Setti

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Maximum Principles on Riemannian Manifolds and Applications

By: Stefano Pigola,Marco Rigoli,Alberto Giulio Setti

Aims to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity obtained by the authors.

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Page Count

118

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821836390

ISBN 13

9780821836392

Vanishing and Finiteness Results in Geometric Analysis

A Generalization of the Bochner Technique

By: Stefano Pigola,Marco Rigoli,Alberto G Setti

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Vanishing and Finiteness Results in Geometric Analysis

A Generalization of the Bochner Technique

By: Stefano Pigola,Marco Rigoli,Alberto G Setti

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Page Count

294

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Springer Science & Business Media

Published Date

ISBN 10

3764386428

ISBN 13

9783764386429

Yamabe-type Equations on Complete, Noncompact Manifolds

By: Paolo Mastrolia,Marco Rigoli,Alberto G Setti

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Yamabe-type Equations on Complete, Noncompact Manifolds

By: Paolo Mastrolia,Marco Rigoli,Alberto G Setti

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Page Count

261

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3034803761

ISBN 13

9783034803762

Maximum Principles on Riemannian Manifolds and Applications

By: Stefano Pigola,Marco Rigoli,Alberto Giulio Setti

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Maximum Principles on Riemannian Manifolds and Applications

By: Stefano Pigola,Marco Rigoli,Alberto Giulio Setti

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118

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821836390

ISBN 13

9780821836392

Book's by Alberto G Setti

Yamabe-type Equations on Complete, Noncompact Manifolds

Yamabe-type Equations on Complete, Noncompact Manifolds

Vanishing and Finiteness Results in Geometric Analysis

Vanishing and Finiteness Results in Geometric Analysis

The Beilinson Complex and Canonical Rings of Irregular Surfaces

The Beilinson Complex and Canonical Rings of Irregular Surfaces

The Legacy of Leon Van Hove

The Legacy of Leon Van Hove

Maximum Principles on Riemannian Manifolds and Applications

Maximum Principles on Riemannian Manifolds and Applications

Vanishing and Finiteness Results in Geometric Analysis

Vanishing and Finiteness Results in Geometric Analysis

Yamabe-type Equations on Complete, Noncompact Manifolds

Yamabe-type Equations on Complete, Noncompact Manifolds

Maximum Principles on Riemannian Manifolds and Applications

Maximum Principles on Riemannian Manifolds and Applications

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