global-analysis-and-the-banach-manifold-of-class-h1-curvers

Riemannian Geometry course project on the manifold H¹(I, M) of class H¹ curves on a Riemannian manifold M and its applications to the geodesics problem

3d4399e3 — Pablo 04/10/2023 07:01

Fixed a typo

65997002 — Pablo 04/10/2023 07:01

Changed the notation for some categories

a17fa3d8 — Pablo 19/02/2023 15:31

Changed the author name

70f73dba — Pablo 07/10/2022 14:44

Fixed the proof of the Sobolev inequalities

72cae0c3 — Pablo 03/10/2022 13:36

Fixed a typo

bbf4cbb0 — Pablo 03/10/2022 03:59

Rebranded ramarks

2fc293f2 — Pablo 03/10/2022 03:56

Improved the proof of the fact that the inclusions are continuous

3df5b009 — Pablo 03/10/2022 03:53

Removed an unnecessary label

8a220889 — Pablo 03/10/2022 03:44

Fixed the proof that the inclusions of section spaces are continuous

d16c8af5 — Pablo 30/08/2022 23:40

Fixed the licensing information

8799a7ed — Pablo 30/08/2022 00:33

Added a README and licesing information

65246e10 — Pablo 30/08/2022 00:31

Added further details on the abstract isomorphism between H¹(gamma* TM) and H¹(I, R^n)

f09d3c96 — Pablo 30/08/2022 00:30

Fixed a small typo

66b9c09f — Pablo 28/08/2022 18:25

Fixed a typo

f947f713 — Pablo 28/08/2022 18:09

Changed the notation for the charts of the tanget bundle of H¹(I, M)

e2062929 — Pablo 28/08/2022 15:02

Added a mention to Smale in the comment on condition (C)

d49430bf — Pablo 27/08/2022 21:49

Minor correction to the section on the Morse index theorem

e9d4b817 — Pablo 27/08/2022 21:43

Fixed the placement of a sentence

a2d3d092 — Pablo 27/08/2022 21:22

Minor improvements to the introduction

376233b2 — Pablo 27/08/2022 19:30

Fixed some typos

1dfc5bb9 — Pablo 27/08/2022 19:26

Fixed a bunch of typos

1126d503 — Pablo 27/08/2022 19:14

Implemented Claudio's suggestions

78de3d7d — Pablo 05/08/2022 15:43

Removed the plan file

a7b92956 — Pablo 05/08/2022 14:09

Removed the dependencies on my personal packages

96e981f5 — Pablo 05/08/2022 00:38

Fixed some typos

245e4a69 — Pablo 02/08/2022 20:09

Configured how footnote numbers are displayed

fc857c29 — Pablo 02/08/2022 20:02

Fixed some typos

96652009 — Pablo 02/08/2022 20:01

Configured the PDF title and author

223342f8 — Pablo 01/08/2022 13:42

Changed the author name

523f5145 — Pablo 01/08/2022 02:02

Fixed some typos

d14391d0 — Pablo 01/08/2022 01:59

Changed the title of the notes

096e8d9c — Pablo 01/08/2022 01:58

Rephrased the comment of Palais' condition (C)

168e4f08 — Pablo 01/08/2022 01:57

Added a conclusion to the last section

e650504d — Pablo 01/08/2022 01:09

Changed the notation for the length function

058d9831 — Pablo 01/08/2022 01:06

Removed \newpage before the references

bedd7677 — Pablo 31/07/2022 17:22

Fixed multiple typos in the third section

cafddd12 — Pablo 31/07/2022 17:21

Fixed multiple typos in the second sections

70c1543f — Pablo 31/07/2022 15:47

Added further justifications for being lazy as fuck

c82d159a — Pablo 31/07/2022 15:35

Rephased some sentences in the introduction

171d2ae1 — Pablo 31/07/2022 15:12

Corrected the statement about energy being a Morse function

aaf432bb — Pablo 31/07/2022 14:44

Fixed some typos

016668de — Pablo 31/07/2022 14:43

Added a clarification on the notion of conjugate points

c3faf106 — Pablo 31/07/2022 14:39

Rephrased the theorem that states that the Morse index of a geodesic is well defined

98369abb — Pablo 31/07/2022 14:33

Fixed some typos, rephrased some sentences and removed unnecessary whitespace

e5185e2c — Pablo 31/07/2022 14:08

Added some comments on the Jacobi-Darboux theorem

c91fa9da — Pablo 30/07/2022 23:10

Changed the statement of the Jacobi-Darboux theorem

f35c307c — Pablo 30/07/2022 23:09

Made it so that the TOC and the introduction section sit on the same page

ec159871 — Pablo 30/07/2022 23:08

Fixed a typo

f0a3ac06 — Pablo 30/07/2022 23:02

Added most of the remaining comments to the final section

5a320435 — Pablo 29/07/2022 23:30

Fixed a typo in a filename

b74e64dc — Pablo 29/07/2022 23:29

Made it so that the table of contents and the references sit on their own pages

f120171c — Pablo 29/07/2022 23:28

Minor tweak

b7942966 — Pablo 29/07/2022 23:28

Added most of the content of the final section

ecccb2fb — Pablo 29/07/2022 00:29

General corrections to last chapter

b6ab57dc — Pablo 28/07/2022 23:35

Fixed a typo

6ffcbd68 — Pablo 28/07/2022 23:35

Removed unnecessary whitespace

78562b87 — Pablo 28/07/2022 23:34

Finished writing the section on the metric of H¹(I, M)

7515687c — Pablo 28/07/2022 13:44

Further clarifications in notation

83cacbee — Pablo 28/07/2022 12:43

Minor clarification

5e7748a2 — Pablo 27/07/2022 22:56

Fixed some typos and removed unecessary whitespace

b38ce71b — Pablo 27/07/2022 22:53

Started to work on the section about the metric of H¹(I, M)

a04f8021 — Pablo 27/07/2022 15:30

Finished describing the charts of H¹(I, M)

a592e9c2 — Pablo 26/07/2022 18:19

Minor corrections

af83b02e — Pablo 26/07/2022 16:37

Added further explanations to the example of the staircase curve

7efff671 — Pablo 26/07/2022 16:26

Added further comments on the topology of tangent spaces

5a997330 — Pablo 26/07/2022 15:54

Finished writing the introduction of the section on the structure of H¹(I, M)

88cab001 — Pablo 26/07/2022 01:23

Started to work on the section about the structure of H¹(I, M)

d7ebecc2 — Pablo 25/07/2022 19:45

Moved the file for the section on the structure of H¹(I, M)

342f6d25 — Pablo 25/07/2022 19:44

Added an item to the TODO list

bab060d5 — Pablo 25/07/2022 19:42

Minor fixes to the language used in the introduction

d64f2f3f — Pablo 25/07/2022 16:25

Removed unnecessary whitespace

ca4ee66e — Pablo 25/07/2022 16:24

Added a reference the paper by Eells in the example about the group of units of a Banach algebra

2929d44d — Pablo 25/07/2022 16:19

Rewrote the introduction of the notes

c105646c — Pablo 25/07/2022 14:31

Mostly finished the section on Banach manifolds

26161254 — Pablo 24/07/2022 14:16

Initial commit