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Extremals for the Sobolev inequality...

Ivanov, Stefan P.

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Extremals for the Sobolev inequality and the quaternionic contact Yamabe problem /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Extremals for the Sobolev inequality and the quaternionic contact Yamabe problem // Stefan P. Ivanov, Dimiter N. Vassilev.
作者:	Ivanov, Stefan P.
其他作者:	Vassilev, Dimiter N.
出版者:	Singapore ;World Scientific, : c2011.,
面頁冊數:	xvii, 219 p. ;24 cm.
標題:	Geometry, Differential. -
ISBN:	9789814295703 (hbk.) :

Extremals for the Sobolev inequality and the quaternionic contact Yamabe problem /
Ivanov, Stefan P.

Extremals for the Sobolev inequality and the quaternionic contact Yamabe problem /Stefan P. Ivanov, Dimiter N. Vassilev. - Singapore ;World Scientific,c2011. - xvii, 219 p. ;24 cm.

Includes bibliographical references (p. 207-216) and index.

Variational problems related to Sobolev inequalities on Carnot groups --Machine generated contents note:

ISBN: 9789814295703 (hbk.) :US89.00Subjects--Topical Terms:

523835
Geometry, Differential.

LC Class. No.: QA649 / .I9 2011

Dewey Class. No.: 516.36

Extremals for the Sobolev inequality and the quaternionic contact Yamabe problem /
LDR:04077cam a2200265 a 4500 001 980864
003 OCoLC
005 20111018102229.0
008 111115s2011 si b 001 0 eng d
020 $a 9789814295703 (hbk.) : $c US89.00
020 $a 9814295701 (hbk.)
029 1 $a DEBSZ $b 330503111
029 1 $a DEBBG $b BV037410388
035 $a (OCoLC)496951750
035 $a AS-BW-100-N-02
040 $a BTCTA $b eng $c BTCTA $d YDXCP $d NUI $d MUU $d SINLB $d INU $d CDX $d UKMGB $d DEBSZ
049 $a FISA
050 # 0 $a QA649 $b .I9 2011
082 0 4 $a 516.36 $2 22
100 1 $a Ivanov, Stefan P. $3 1306047
245 1 0 $a Extremals for the Sobolev inequality and the quaternionic contact Yamabe problem / $c Stefan P. Ivanov, Dimiter N. Vassilev.
260 # $a Singapore ; $a Hackensack, NJ : $b World Scientific, $c c2011.
300 $a xvii, 219 p. ; $c 24 cm.
504 $a Includes bibliographical references (p. 207-216) and index.
505 0 0 $g Machine generated contents note: $g 1. $t Variational problems related to Sobolev inequalities on Carnot groups -- $g 1.1. $t Introduction -- $g 1.2. $t Carnot groups -- $g 1.3. $t Sobolev spaces and their weak topologies -- $g 1.4. $t The best constant in the Folland-Stein inequality -- $g 1.5. $t The best constant in the presence of symmetries -- $g 1.6. $t Global regularity of weak solutions -- $g 1.6.1. $t Global boundedness of weak solutions -- $g 1.6.2. $t The Yamabe equation -- Cinfinity regularity of weak solutions -- $g 2. $t Groups of Heisenberg and Iwasawa types explicit solutions to the Yamabe equation -- $g 2.1. $t Introduction -- $g 2.2. $t Groups of Heisenberg and Iwasawa types -- $g 2.3. $t The Cayley transform, inversion and Kelvin transform -- $g 2.3.1. $t The Cayley transform -- $g 2.3.2. $t Inversion on groups of Heisenberg type -- $g 2.3.3. $t The Kelvin transform -- $g 2.4. $t Explicit entire solutions of the Yamabe equation on groups of Heisenberg type -- $g 3. $t Symmetries of solutions on groups of Iwasawa type -- $g 3.1. $t Intoduction -- $g 3.2. $t The Hopf Lemma
505 0 0 $g 3.3. $t The partially symmetric solutions have cylindrical symmetry -- $g 3.4. $t Determination of the cylindrically symmetric solutions of the Yamabe equation -- $g 3.5. $t Solution of the partially symmetric Yamabe problem -- $g 3.6. $t Applications. Euclidean Hardy-Sobolev inequalities -- $g 3.6.1. $t A non-linear equation in Rn related to the Yamabe equation on groups of Heisenberg type -- $g 3.6.2. $t The best constant and extremals of the Hardy-Sobolev inequality -- $g 4. $t Quaternionic contact manifolds -- Connection, curvature and qc-Einstein structures -- $g 4.1. $t Introduction -- $g 4.2. $t Quaternionic contact structures and the Biquard connection -- $g 4.3. $t The curvature of the Biquard connection -- $g 4.3.1. $t The first Bianchi identity and Ricci tensors -- $g 4.3.2. $t Local structure equations of qc manifolds -- $g 4.3.3. $t The curvature tensor -- $g 4.3.4. $t The flat model -- The qc Heisenberg group -- $g 4.4. $t qc-Einstein quaternionic contact structures -- $g 4.4.1. $t Examples of qc-Einstein structures -- $g 4.4.2. $t Cones over a quaternionic contact structure -- $g 5. $t Quaternionic contact conformal curvature tensor
505 0 0 $g 5.1. $t Introduction -- $g 5.2. $t Quaternionic contact conformal transformations -- $g 5.2.1. $t The quaternionic Cayley transform -- $g 5.3. $t qc conformal curvature -- $g 6. $t The quaternionic contact Yamabe problem and the Yamabe constant of the qc spheres -- $g 6.1. $t Introduction -- $g 6.2. $t Some background -- $g 6.2.1. $t The qc normal frame -- $g 6.2.2. $t Horizontal divergence theorem -- $g 6.2.3. $t Conformal transformations of the quaternionic Heisenberg group preserving the vanishing of the torsion -- $g 6.3. $t Constant qc scalar curvature and the divergence formula -- $g 6.4. $t Divergence formulas -- $g 6.5. $t The divergence theorem in dimension seven -- $g 6.6. $t The qc Yamabe problem on the qc sphere and quaternionic Heisenberg group in dimension seven -- $g 6.7. $t The qc Yamabe constant on the qc sphere and the best constant in the Folland-Stein embedding on the quaternionic Heisenberg group -- $g 7. $t CR manifolds -- Cartan and Chern-Moser tensor and theorem -- $g 7.1. $t Introduction -- $g 7.2. $t CR-manifolds and Tanaka-Webster connection -- $g 7.3. $t The Cartan-Chern-Moser theorem -- $g 7.3.1. $t The three dimensional case.
650 # 0 $a Geometry, Differential. $3 523835
650 # 0 $a Contact manifolds. $3 731203
650 # 0 $a Group theory. $3 523248
700 1 # $a Vassilev, Dimiter N. $3 1306048