Perspectves in Scalar Curvature

In 2 Volumes

Mikhail L Gromov Insttut des Hautes Études Scientfques, France

H Blaine Lawson, Jr. Stony Brook University, USA

Key Features

• his is a wide ranging work centered on the sub ect, rom geometr , o scalar curvature. t begins with a long artcle wri en b isha Gromov with man topics and open problems. he rest o olume consists o artcles wri en about ver recent ma or advances, b people involved in these discoveries. olume 2 is a diverse and ascinatng collecton o essa s wri en b mathematcians and ph sicists about their view o scalar curvature in their own work. he were invited to write whatever the ound appealing. Some wrote large surve s and others wrote artcles that were specifcall ocused. he ensemble is e tremel interestng

• ne reason this book is needed is that it put together viewpoints on scalar curvature rom man uite di erent perspectves. t seems likel that this will engender new thinking in man areas

• Certainl the contributors are all leading researchers, and ver well known

Descripton

Volume I contains a long artcle by Misha Gromov based on his many years of involvement in this subject. t came rom lectures delivered in Spring 20 9 at HES. here is some background given. an topics in the feld are presented, and man open problems are discussed. ne intriguing point here is the crucial role pla ed b two seemingl unrelated anal tc means inde theor o irac operators and geometric measure theor .

er recentl there have been some real breakthroughs in the feld. olume has several surve artcles wri en b people who were responsible or these results.

or olume , man people in areas o mathematcs and ph sics, whose work is somehow related to scalar curvature, were asked to write about this in an wa tha pleased. his gives rise to a wonder ul collecton o artcles, some with ver broad and historical views, others which discussed specifc ascinatng sub ects.

hese two books give a rich and power ul view o one o geometr s ver appealing sides.

Editors

Misha Gromov, a Gould Pro essor o athematcs at Courant nsttute, U, and emeritus pro essor at HES, rance. Ph rom Leningrad State Universit in 969. esearch interests spaces o geometric structures on mani olds and o spaces o maps between mani olds iemannian geometr , s mplectc geometr , combinatorial geometr , as mptotc geometr o infnite groups mathematcal structures underl ing living organisms and their ph siological and mental unctons including human natural languages.

H Blaine Lawson, r., istnguished Pro essor, Ston rook Universit , Ston rook, . inimal sur aces in the 3 sphere, oliatons o spheres, boundaries o comple anal tc varietes and holomorphic chains, co creator o the feld o calibrated geometries, work with Gromov on positve scalar curvature, work on algebraic c cles and homotop theor .

January 2023

Imprint: World Scientfc Publishing Compan

Extent: 636pp

Type: eview olume

Main Subject: athematcs

Sub-Subjects: Geometr (Conve nd iscrete Geometr ) nd opolog

Global nal sis nal sis n ani olds elatvit Gravitaton

Keywords: Scalar Curvature irac perators nde o irac perators oo Genus Spin ani olds K heor Lichnerowic ormula acroscopic imension inimal H persu aces Positve ass heorems omininant Energ Conditon uasi Local ass iemannian Pol hedra and Width Enlargeable ani olds Callias perators Waist ne ualit C lgebras and K theor

Readership: Pro essional mathematcians and ph sicists, and certainl graduate students, in di erental geometr and related areas in mathematcs, and in general relatvit and related areas in ph sics. he books could easil be used or advanced graduate courses in mathematcs and ph sics

• Volume I:

◊ Four Lectures on Scalar Curvature

◊ Scalar Curvature and Generalized Callias Operators

◊ Convergence and Regularity of Manifolds with Scalar Curvature and Entropy Lower Bounds

◊ Level Set Methods in the Study of Scalar Curvature

◊ The Secret Hyperbolic Life of Positve Scalar Curvature

◊ On the Scalar Curvature of 4-Manifolds

• Volume II:

◊ Classical Relatons to Topology and the Dirac Operator: Some Topological Implicatons of Positve Scalar Curvature and Generalizatons Complete Manifolds with Positve Scalar Curvature

Manifolds with Boundary and Spaces of Metrics with Positve Scalar Curvature and Mean Curvature

Minimal Varietes

◊ Positve Mass and Positve Energy

◊ Positve Scalar Curvature on Generalized Spaces: Pol hedra and Positve Scalar Curvature on etric Spaces istance Estmates amilies and oliatons