Three Extremal Problems for Hyperbolically Convex Functions - PowerPoint PPT Presentation

About This Presentation
Title:

Three Extremal Problems for Hyperbolically Convex Functions

Description:

Three Extremal Problems for Hyperbolically Convex Functions Roger W. Barnard, Kent Pearce, G. Brock Williams Texas Tech University [Computational Methods and Function ... – PowerPoint PPT presentation

Number of Views:66
Avg rating:3.0/5.0
Slides: 40
Provided by: Kent259
Learn more at: https://www.math.ttu.edu
Category:

less

Transcript and Presenter's Notes

Title: Three Extremal Problems for Hyperbolically Convex Functions


1
Three Extremal Problems for Hyperbolically
Convex Functions
  • Roger W. Barnard, Kent Pearce, G. Brock Williams
  • Texas Tech University
  • Computational Methods and Function Theory 4
  • (2004) pp 97-109

2
Notation Definitions

3
Notation Definitions

4
Notation Definitions
  • Hyberbolic Geodesics

5
Notation Definitions
  • Hyberbolic Geodesics
  • Hyberbolically Convex Set

6
Notation Definitions
  • Hyberbolic Geodesics
  • Hyberbolically Convex Set
  • Hyberbolically Convex Function

7
Notation Definitions
  • Hyberbolic Geodesics
  • Hyberbolically Convex Set
  • Hyberbolically Convex Function
  • Hyberbolic Polygon
  • o Proper Sides

8
Classes

9
Classes

10
Classes

11
Classes

12
Examples

13
Problems
  • 1.

14
Problems
  • 1.
  • 2.
  • Find

15
Problems
  • 1.
  • 2.
  • Find
  • 3.

16
Theorem 1

17
Theorem 2
  • Remark Minda Ma observed that cannot be
    extremal
  • for

18
Theorem 3

19
Julia Variation

20
Julia Variation (cont.)

21
Julia Variation (cont.)

22
Variations for (Var. 1)

23
Variations for (Var. 2)

24
Proof (Theorem 1)

25
Proof (Theorem 1)

26
Proof (Theorem 1)

27
Proof (Theorem 1)
  • From the Calculus of Variations

28
Proof (Theorem 1)

29
Proof (Theorem 1)

30
Proof (Theorem 1)

31
Proof (Theorem 1)

32
Proof (Theorem 1)

33
Proof (Theorem 1)

34
Proof (Theorem 1)

35
Proof (Theorem 1)

36
Proof (Theorem 1)

37
Proof (Theorem 1)

38
Proof (Theorem 1)

39
Proofs (Theorem 2 3)
Write a Comment
User Comments (0)
About PowerShow.com