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 .

February 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

Fractonal Diferental Equatons and Inclusions

Classical and Advanced Topics

Saïd Abbas

Tahar Moulay University of Saida, Algeria

Moufak Benchohra

Djillali Liabes University of Sidi Bel-Abbes, Algeria

Jamal Eddine Lazreg

Djillali Liabes University of Sidi Bel-Abbes, Algeria

Key Features

Juan J Nieto (Universidade de Santago de Compostela, Spain

Yong Zhou Xiangtan University, China & Macau University of Science and Technology, China

• his monograph is devoted to the e istence and stabilit or various classes o unctonal di erental e uatons or inclusions involving the Hadamard or Hil er ractonal derivatve. here are onl a ew s stematc discussions on these contents in published books

• an new results are presented and this represents the main di erence between this book and compettve ttles

• good supplement to the e istng literature on ractonal di erental e uatons

Descripton

This monograph is devoted to the existence and stability (Ulam–Hyers–Rassias stability and asymptotc stability) of solutons for various classes of functonal diferental equatons or inclusions involving the Hadamard or Hilfer fractonal derivatve. Some e uatons present dela which ma be fnite, infnite, or state dependent. thers are sub ect to impulsive e ect which ma be f ed or non instantaneous.

eaders will fnd the book sel contained and unifed in presentaton. t provides the necessar background material re uired to go urther into the sub ect and e plores the rich research literature in detail. Each chapter concludes with a secton devoted to notes and bibliographical remarks and all abstract results are illustrated b e amples. he tools used include man classical and modern nonlinear anal sis methods such as f ed point theorems, as well as some notons o Ulam stabilit , a ractvit and the measure o non compactness as well as the measure o weak noncompactness. t is use ul or researchers and graduate students or research, seminars, and advanced graduate courses, in pure and applied mathematcs, ph sics, mechanics, engineering, biolog , and all other applied sciences.

Authors

Dr Saïd Abbas is a ull Pro essor at the department o mathematcs at ahar oula Universit o Saida since ctober 2006. bbas received the master s degree in unctonal nal sis rom ostaganem Universit , lgeria, 2006, and the doctorate s degree in i erental E uatons rom illali Liabes Universit o Sidi el bbes, lgeria, 20 .

Dr Moufak Benchohra is a ull Pro essor at the department o mathematcs, illali Liabes Universit o Sidi el bbes since ctober 994. enchohra received the master s degree in onlinear nal sis rom lemcen Universit , lgeria, 994 and Ph. . degree in athematcs rom illali Liabes Universit , Sidi el bbes, lgeria.

February 2023

Imprint: World Scientfc Publishing Compan

Extent: 270pp

Type: onograph

Series: Series on nal sis, pplicatons and Computaton Volume 10

Main Subject: athematcs

Sub-Subjects: rdinar i erental

E uatons ntegral E uatons

Keywords: ractonal Calculus

Hadamard and Hil er ractonal i erental E uatons Caputo

Hadamard ractonal i erental

E uatons Hil er ractonal i erental

E uatons Hil er Hadamard ractonal i erental E uatons Hil er Hadamard ractonal i erental nclusions

Hil er ractonal i erental nclusions

Hil er Pe s ractonal i erental

E uatons mplicit Hil er Pe s ractonal i erental E uatons mplicit

Hadamard Pe s ractonal i erental

E uatons Hadamard Pe s ractonal ntegral E uatons ractvit Stabilit s mptotc Stabilit E istence Global

Stabilit Ulam Stabilit

Readership: esearchers and graduate students or research, seminars, and advanced graduate courses, in pure and applied mathematcs, ph sics, mechanics, engineering, biolog , and other applied sciences

• Preliminar ackground

• Hadamard and Hil er ractonal i erental E uatons and nclusions

• ractvit esults or Hil er ractonal i erental E uatons

• Ulam Stabilit esults or Hil er ractonal i erental E uatons and nclusions

• andom Hil er ractonal i erental E uatons and nclusions

• onlinear Hadamard Pe s ractonal ntegral E uatons

• onlinear mplicit Hadamard Pe s ractonal i erental E uatons

• Hil er Pe s ractonal i erental E uatons and nclusions

• mplicit Hil er Pe s ractonal i erental E uatons