Singular sets of minimizers for the Mumford-Shah functional:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2005
|
| Series: | Progress in Mathematics
233 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 581 S. graph. Darst. |
| ISBN: | 376437182X |
Staff View
MARC
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| 100 | 1 | |a David, Guy |d 1957- |e Verfasser |0 (DE-588)112614086 |4 aut | |
| 245 | 1 | 0 | |a Singular sets of minimizers for the Mumford-Shah functional |c Guy David |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2005 | |
| 300 | |a XIV, 581 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in Mathematics |v 233 | |
| 650 | 7 | |a Calculo de variações |2 larpcal | |
| 650 | 7 | |a Controle ótimo |2 larpcal | |
| 650 | 7 | |a Equações diferenciais |2 larpcal | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Calculus of variations | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Geometric measure theory | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 0 | 7 | |a Minimierung |0 (DE-588)4251074-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mumford-Shah-Funktional |0 (DE-588)4688496-8 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804133118418878464 |
|---|---|
| adam_text | GUY DAVID
SINGULAR SETS O
F MINIMIZER
S
FO
R TH
E
MUMFORD-SHA
H FUNCTIONA
L
BIRKHAUSER VERLAG
BASEL YY BOSTON YY BERLIN
CONTENTS
FOREWORD XI
A PRESENTATION OF THE MUMFORD-SHAH FUNCTIONAL
1 TH
E MUMFORD-SHA
H FUNCTIONAL AN
D IMAGE SEGMENTATIO
N 1
2 DEFINITION OF TH
E FUNCTIONAL 5
3 MINIMIZING IN
U
WIT
H
K
FIXED 8
4
H
N
~
1
IS NO
T SEMICONTINUOU
S BU
T
J
HA
S MINIMIZERS 11
5 SIMPLE EXAMPLES
, N
O UNIQUENESS
, BU
T FEW BUTTERFLIE
S
IN HONG-KONG 14
6 TH
E MUMFORD-SHA
H CONJECTUR
E AN
D SOME KNOWN RESULT
S 30
7 MAN
Y DEFINITIONS OF ALMOST
- AN
D QUASIMINIMIZER
S 36
8 REDUCE
D MINIMIZERS AN
D PAIRS
, CORA
L PAIR
S 50
B FUNCTIONS IN THE SOBOLEV SPACES
W
1
^
9 ABSOLUT
E CONTINUIT
Y ON LINES 63
10 SOME REMOVABLE SET
S FOR
W
LTP
67
11 COMPOSITIO
N WIT
H OTHE
R FUNCTIONS 71
12 POINCAR
E ESTIMATE
S FOR / G
W^
P
{Q)
75
13 BOUNDAR
Y VALUES AN
D RESTRICTION
S T
O HYPERSURFACES 80
14 A SIMPLE WELDING LEMM
A 86
15 ENERGY-MINIMIZIN
G FUNCTIONS WIT
H PRESCRIBE
D BOUNDAR
Y VALUES ..
. 90
16 ENERG
Y MINIMIZERS FOR A
N INCREASIN
G UNIO
N OF OPE
N SET
S 95
17 CONFORMAL INVARIANCE AN
D TH
E NEUMAN
N CONDITIO
N 98
C REGULARITY PROPERTIES FOR QUASIMINIMIZERS
18 LOCAL AHLFORS-REGULARITY
: TH
E STATEMENT
S 105
19 A SMAL
L DENSIT
Y RESUL
T 113
20 PROO
F OF LOCAL AHLFORS-REGULARIT
Y IN DIMENSIO
N 2: TH
E SCHEME ...
. 114
21 ENERG
Y ESTIMATE
S FOR TH
E AHLFORS-REGULARIT
Y RESUL
T (N = 2) 122
22 SIMPLE ESTIMATE
S ON TH
E POISSON KERNEL *. . 137
23 CARLESO
N MEASURE
S 143
VIII CONTENTS
24 TH
E PROPERT
Y OF PROJECTION
S (
N = 2) 148
25 TH
E CONCENTRATIO
N PROPERT
Y (N = 2) 155
26 AVERAGE NUMBE
R OF POINT
S ON A CIRCLE 160
27 UNIFORM RECTIFIABILITY WHE
N
N
= 2 163
28 TH
E CO-ARE
A FORMULA 168
29
K
CONTAIN
S BIG PIECES OF CONNECTE
D SET
S LOCALLY 170
30 SIMPLE ARC
S IN CONNECTE
D SET
S WIT
H FINITE I
F ^MEASUR
E 186
31 BIG PIECES OF CONNECTE
D SET
S AN
D UNIFORM RECTIFIABILITY 191
32 APPLICATIO
N T
O QUASIMINIMIZER
S AN
D A TEMPORAR
Y CONCLUSION ...
. 204
D LIMITS OF ALMOST-MINIMIZERS
33 VITALI COVERING LEMMAS 207
34 LOCAL HAUSDORFF CONVERGENCE OF SETS 213
35 UNIFORM CONCENTRATION AND LOWER SEMICONTINUITY
OF HAUSDORFF MEASURE 217
36 A LITTLE MORE ON TH
E EXISTENCE OF MINIMIZERS 222
37 LIMITS OF ADMISSIBLE PAIRS 227
38 LIMITS OF LOCAL ALMOST-MINIMIZERS ARE LOCAL
TOPOLOGICAL ALMOST-MINIMIZERS 234
39 LIMITS OF ALMOST-MINIMIZERS UP T
O TH
E BOUNDARY 257
40 BLOW-UP LIMITS 266
E
PIECES OF
C
1
CURVES
FOR ALMOST-MINIMIZERS
41 UNIFORM RECTIFIABILITY, TH
E PETER JONES NUMBERS
F3(X,R),
AND WHY
K
IS FLAT IN MANY PLACES 272
42 LOWER BOUNDS ON TH
E JUM
P OF
U
WHEN
K
IS FLAT
AND VU IS SMALL 278
43 NORMALIZED JUMP
S OFTEN TEND T
O GET LARGER 282
44 ON THE SIZE OF TH
E HOLES IN
K
284
45
U)*(X,R)
(SOMETIMES WITH FLATNESS) CONTROLS TH
E SURFACE
AND ENERGY INSIDE 288
46 SIMPLE CONSEQUENCES WHEN
N
= 2, AND TH
E EXISTENCE
OF GOOD DISKS 293
47 BONNET S LOWER BOUND ON TH
E DERIVATIVE OF ENERGY 297
48 THE MAIN ESTIMATE ON TH
E DECAY OF TH
E NORMALIZED
ENERGY
U)2{X, R) (N =
2) 310
49 SELF-IMPROVING SETS OF ESTIMATES (N = 2) 315
50 THREE CONDITIONS FOR
K
T
O CONTAIN A NICE CURVE
(N =
2) 321
51
K
( I
B{X, R)
IS OFTEN A NICE C
1
CURVE (N = 2) 332
52 JUM
P AND FLATNESS CONTROL SURFACE AND ENERGY *. 338
53 SIMILAR RESULTS WITH SPIDERS AND PROPELLERS
(N
= 2) 344
CONTENTS IX
F GLOBAL MUMFORD-SHAH MINIMIZERS IN THE PLANE
54 GLOBA
L MINIMIZER
S IN
RYY AN
D A VARIAN
T
OF TH
E MUMFORD-SHA
H CONJECTUR
E 355
55 NO BOUNDE
D CONNECTE
D COMPONEN
T I
N IR
2
K
362
56 NO THI
N CONNECTE
D COMPONEN
T IN
M
2
K
EITHER
; JOH
N DOMAIN
S . . . 367
57 EVER
Y NONTRIVIA
L CONNECTE
D COMPONEN
T OF
K
IS A CHORD-AR
C TRE
E 370
58 TH
E CASE WHEN
U
IS LOCALLY CONSTAN
T SOMEWHERE (N = 2) 380
59 SIMPLE FACTS ABOU
T LINES AN
D PROPELLERS
; BLOW-IN LIMIT
S 391
60 ANOTHE
R REGULARIT
Y RESUL
T FOR LOCAL ALMOST-MINIMIZERS
;
POINT
S OF LOW ENERG
Y 396
61 BONNET
S THEORE
M ON CONNECTE
D GLOBAL MINIMIZERS 401
62 CRACKTI
P IS A GLOBAL MINIMIZER 414
63 TH
E MAGIC FORMULA WIT
H (|^)
2
IN TERM
S OF
K
431
64 TH
E CASE WHEN
K
IS CONTAINE
D IN A COUNTABL
E UNIO
N OF LINES ...
. 442
65 ANOTHE
R FORMULA, WIT
H RADIA
L AN
D TANGENTIA
L DERIVATIVE
S 447
66 K
2
K
IS CONNECTE
D WHE
N
(U, K)
IS A
N EXOTI
C GLOBAL MINIMIZER . . . 453
67 POINT
S OF HIGH ENERGY, TH
E SINGULA
R SINGULA
R SET
K^
463
G APPLICATIONS T
O ALMOST-MINIMIZERS
(
N = 2)
68 NO SMAL
L LOOP IN
K,
TH
E CHORD-AR
C AN
D TH
E JOH
N CONDITION
S ...
. 469
69 SPIRAL POINT
S 475
70 TW
O LAST REGULARIT
Y RESULT
S 489
71 FROM TH
E MUMFORD-SHA
H CONJECTUR
E IN TH
E PLAN
E
T
O IT
S LOCAL VERSION 493
H QUASI- AND ALMOST-MINIMIZERS IN HIGHER DIMENSIONS
72 LOCAL AHLFORS-REGULARITY FOR QUASIMINIMIZER
S 495
73 UNIFORMLY RECTIFIABLE SET
S OF ALL DIMENSION
S 512
74 UNIFORM RECTIFIABILITY FOR QUASIMINIMIZER
S 518
75
C
1
REGULARIT
Y ALMOST-EVERYWHER
E FOR ALMOST-MINIMIZER
S 523
76 WHA
T IS A MUMFORD-SHA
H CONJECTUR
E IN DIMENSION 3? 528
I BOUNDARY REGULARITY
77 AHLFORS-REGULARITY NEA
R TH
E BOUNDAR
Y 539
78 A REFLECTION TRIC
K 551
79 BOUNDAR
Y REGULARIT
Y FOR ALMOST-MINIMIZER
S IN DIMENSION 2 559
80 A FEW QUESTION
S 570
REFERENCES
573
INDEX
579
|
| any_adam_object | 1 |
| author | David, Guy 1957- |
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| discipline | Mathematik |
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| id | DE-604.BV019679467 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:03:38Z |
| institution | BVB |
| isbn | 376437182X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013007474 |
| oclc_num | 57893734 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-11 DE-188 DE-29T |
| owner_facet | DE-91G DE-BY-TUM DE-11 DE-188 DE-29T |
| physical | XIV, 581 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in Mathematics |
| series2 | Progress in Mathematics |
| spelling | David, Guy 1957- Verfasser (DE-588)112614086 aut Singular sets of minimizers for the Mumford-Shah functional Guy David Basel [u.a.] Birkhäuser 2005 XIV, 581 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in Mathematics 233 Calculo de variações larpcal Controle ótimo larpcal Equações diferenciais larpcal Boundary value problems Calculus of variations Differential equations, Partial Geometric measure theory Manifolds (Mathematics) Minimierung (DE-588)4251074-0 gnd rswk-swf Mumford-Shah-Funktional (DE-588)4688496-8 gnd rswk-swf Mumford-Shah-Funktional (DE-588)4688496-8 s Minimierung (DE-588)4251074-0 s DE-604 Progress in Mathematics 233 (DE-604)BV000004120 233 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013007474&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | David, Guy 1957- Singular sets of minimizers for the Mumford-Shah functional Progress in Mathematics Calculo de variações larpcal Controle ótimo larpcal Equações diferenciais larpcal Boundary value problems Calculus of variations Differential equations, Partial Geometric measure theory Manifolds (Mathematics) Minimierung (DE-588)4251074-0 gnd Mumford-Shah-Funktional (DE-588)4688496-8 gnd |
| subject_GND | (DE-588)4251074-0 (DE-588)4688496-8 |
| title | Singular sets of minimizers for the Mumford-Shah functional |
| title_auth | Singular sets of minimizers for the Mumford-Shah functional |
| title_exact_search | Singular sets of minimizers for the Mumford-Shah functional |
| title_full | Singular sets of minimizers for the Mumford-Shah functional Guy David |
| title_fullStr | Singular sets of minimizers for the Mumford-Shah functional Guy David |
| title_full_unstemmed | Singular sets of minimizers for the Mumford-Shah functional Guy David |
| title_short | Singular sets of minimizers for the Mumford-Shah functional |
| title_sort | singular sets of minimizers for the mumford shah functional |
| topic | Calculo de variações larpcal Controle ótimo larpcal Equações diferenciais larpcal Boundary value problems Calculus of variations Differential equations, Partial Geometric measure theory Manifolds (Mathematics) Minimierung (DE-588)4251074-0 gnd Mumford-Shah-Funktional (DE-588)4688496-8 gnd |
| topic_facet | Calculo de variações Controle ótimo Equações diferenciais Boundary value problems Calculus of variations Differential equations, Partial Geometric measure theory Manifolds (Mathematics) Minimierung Mumford-Shah-Funktional |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013007474&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT davidguy singularsetsofminimizersforthemumfordshahfunctional |