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1 An analogue of the Euler formula |
12-17 |
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1.1 Introduction and basic concepts |
12-14 |
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1.2 preliminary |
14-15 |
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1.3 prove the conclusion |
15-17 |
|
2 The bonnesen-type inequality on constant plane |
17-30 |
|
2.1 Basic concepts of convex sets in Euclidean space |
18-20 |
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2.1.1 Basic concepts of convex sets and convex curves |
18 |
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2.1.2 Support lines and their existence |
18-20 |
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2.2 Measure for sets and formulas of integral geometry |
20-25 |
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2.2.1 Measure for sets of geometric elements |
20-22 |
|
measure for sets of points |
20-21 |
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Measure for sets of lines |
21-22 |
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2.2.2 Formulas of integral geometry in the plane |
22-25 |
|
The group of motion |
22-23 |
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The differential form on G |
23-24 |
|
The kinematic density |
24-25 |
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Poincare's formula and Blaschke formula |
25 |
|
2.3 Isoperimetric inequality |
25-30 |
|
2.3.1 Isoperimetric inequality |
25-26 |
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2.3.2 stronger isoperimetric inequalities |
26-28 |
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2.3.3 An upper limit for isoperimetric deficit |
28-30 |
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3 conclusions |
30-40 |
|
3.1 Bonnesen-type inequality in non-Euclidean plane |
30-37 |
|
3.1.1 some preliminaries and concepts |
30-32 |
|
3.1.2 Bonnesen-type inequalitise in the hyperbolic plane H~2 |
32-35 |
|
3.1.3 Bonnesen-type inequalities in projective plane PR~2 |
35-37 |
|
3.2 An upper limit in constant plane |
37-40 |
|
3.2.1 the kinematic formula in constant plane |
37-38 |
|
3.2.2 An upper limits in non-Euclidean plane |
38-40 |
|
An upper limits in hyperbolic plane |
38-39 |
|
An upper limits in projective plane |
39-40 |
|
Bibliography |
40-43 |
|
原创性声明 |
43 |
|
关于学位论文使用授权的声明 |
43 |
