Contents
Preface i x
Chapter 1. Hyperplan e section s o f £ p-bal\s 1
1.1. Lectur e 1 1
Chapter 2 . Volum e an d th e Fourie r transfor m 9
2.1. Lectur e 2 9
Chapter 3 . Intersectio n bodie s 2 1
3.1. Lectur e 3 2
3.2. Intersectio n bodie s an d ellipsoid s 2 6
3.3. Non-intersectio n bodie s al l o f whos e centra l section s ar e
intersection bodie s 3 0
3.4. Generalize d intersectio n bodie s 3 3
Chapter 4 . Th e Busemann-Pett y proble m 3 9
4.1. Lectur e 4 3 9
4.2. A modification o f the Busemann-Pett y proble m 4 3
4.3. Th e Busemann-Pett y proble m i n hyperboli c an d spherica l
Spaces 4 5
4.4. Th e lowe r dimensiona l Busemann-Pett y proble m 5 5
Chapter 5 . Projection s an d th e Fourie r transfor m 5 9
5.1. Lectur e 5 5 9
Chapter 6 . Intersectio n bodie s an d L p-spaces 6 7
6.1. Lectur e 6 6 7
Chapter 7 . O n th e roa d betwee n pola r projectio n bodie s an d
intersection bodie s 7 5
7.1. Lectur e 7 7 5
7.2. Th e geometr y o f L
0
7 7
7.3. A Banach subspac e o f L 1/2 tha t doe s not embe d i n L\ 8 0
7.4. Commo n subspace s o f L
p
Space s 8 4
Chapter 8 . Ope n problem s 8 7
Bibliography 10
Index 107
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