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The Resource Integral Geometry and Valuations, by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes, (electronic resource)

Integral Geometry and Valuations, by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes, (electronic resource)

Creator
Author
Editor
Contributor
Summary
Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented in the first part. At the core of this approach lies the close relationship between kinematic formulas and Alesker's product of valuations. This original viewpoint not only enlightens the classical integral geometry of Euclidean space, it has also produced previously unreachable results, such as the explicit computation of kinematic formulas in Hermitian spaces
Language
eng
Work
Publication
Extent
VIII, 112 p.
Contents
  • Part I: New Structures on Valuations and Applications
  • Translation invariant valuations on convex sets
  • Valuations on manifolds
  • Part II: Algebraic Integral Geometry
  • Classical integral geometry
  • Curvature measures and the normal cycle
  • Integral geometry of euclidean spaces via Alesker theory
  • Valuations and integral geometry on isotropic manifolds
  • Hermitian integral geometry
Isbn
9783034808743
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0874-3
Instance
Label
Integral Geometry and Valuations
Title
Integral Geometry and Valuations
Statement of responsibility
by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes
Creator
Contributor
Author
Editor
Subject
Language
eng
Summary
Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented in the first part. At the core of this approach lies the close relationship between kinematic formulas and Alesker's product of valuations. This original viewpoint not only enlightens the classical integral geometry of Euclidean space, it has also produced previously unreachable results, such as the explicit computation of kinematic formulas in Hermitian spaces
Member of
http://library.link/vocab/creatorName
Alesker, Semyon
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Fu, Joseph H.G.
  • Gallego, Eduardo.
  • Solanes, Gil.
  • SpringerLink (Online service)
Series statement
Advanced Courses in Mathematics - CRM Barcelona,
http://library.link/vocab/subjectName
  • Mathematics
  • Convex geometry
  • Discrete geometry
  • Differential geometry
Label
Integral Geometry and Valuations, by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0874-3
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Part I: New Structures on Valuations and Applications -- Translation invariant valuations on convex sets -- Valuations on manifolds -- Part II: Algebraic Integral Geometry -- Classical integral geometry -- Curvature measures and the normal cycle -- Integral geometry of euclidean spaces via Alesker theory -- Valuations and integral geometry on isotropic manifolds -- Hermitian integral geometry
Control code
978-3-0348-0874-3
Dimensions
unknown
Extent
VIII, 112 p.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783034808743
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-0348-0874-3
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)893857980
Label
Integral Geometry and Valuations, by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0874-3
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Part I: New Structures on Valuations and Applications -- Translation invariant valuations on convex sets -- Valuations on manifolds -- Part II: Algebraic Integral Geometry -- Classical integral geometry -- Curvature measures and the normal cycle -- Integral geometry of euclidean spaces via Alesker theory -- Valuations and integral geometry on isotropic manifolds -- Hermitian integral geometry
Control code
978-3-0348-0874-3
Dimensions
unknown
Extent
VIII, 112 p.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783034808743
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-0348-0874-3
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)893857980

Subject

Member of

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