LEADER 01108nam--2200361---450- 001 990001803190203316 005 20050513155535.0 010 $a3-631-37200-0 035 $a000180319 035 $aUSA01000180319 035 $a(ALEPH)000180319USA01 035 $a000180319 100 $a20040630d2001----km-y0enga50------ba 101 0 $ager 102 $aDE 105 $ay|||z|||001yy 200 1 $aEinführung in Sprechwissenschaft und Sprecherziehung$fNorbert Gutenberg 210 $aFrankfurt am Main [etc.]$cPeter Lang$d2001 215 $a339 p.$d21 cm. 606 0 $aLinguaggio$xApprendimento 606 0 $aComunicazione orale 676 $a401.93 700 1$aGUTENBERG,$bNorbert$0563738 801 0$aIT$bsalbc$gISBD 912 $a990001803190203316 951 $aIV.2. 1001(XII A 95)$b168458 L.M.$cXII A$d00086738 959 $aBK 969 $aUMA 979 $aACQUISTI$b10$c20040630$lUSA01$h0947 979 $aRENATO$b90$c20041025$lUSA01$h1239 979 $aCOPAT2$b90$c20050513$lUSA01$h1555 996 $aEinführung in Sprechwissenschaft und Sprecherziehung$9951525 997 $aUNISA LEADER 06458nam 22006973 450 001 9910966324603321 005 20231110213201.0 010 $a9781470470920 010 $a1470470926 035 $a(CKB)5600000000455451 035 $a(MiAaPQ)EBC29731903 035 $a(Au-PeEL)EBL29731903 035 $a(OCoLC)1343250800 035 $a(EXLCZ)995600000000455451 100 $a20220905d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLocal Lp-Brunn-Minkowski inequalities for p < 1 /$fAlexander V. Kolesnikov, Emanuel Milman 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2022. 210 4$d©2022. 215 $a1 online resource (90 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.277 311 08$a9781470451608 311 08$a1470451603 327 $aCover -- Title page -- Chapter 1. Introduction -- 1.1. Previously Known Partial Results -- 1.2. Main Results -- 1.3. Spectral Interpretation via the Hilbert-Brunn-Minkowski operator -- 1.4. Method of Proof -- 1.5. Applications -- Chapter 2. Notation -- Chapter 3. Global vs. Local Formulations of the ^{ }-Brunn-Minkowski Conjecture -- 3.1. Standard Equivalent Global Formulations -- 3.2. Global vs. Local ^{ }-Brunn-Minkowski -- Chapter 4. Local ^{ }-Brunn-Minkowski Conjecture -Infinitesimal Formulation -- 4.1. Mixed Surface Area and Volume of ² functions -- 4.2. Properties of Mixed Surface Area and Volume -- 4.3. Second ^{ }-Minkowski Inequality -- 4.4. Comparison with classical =1 case -- 4.5. Infinitesimal Formulation On ??¹ -- 4.6. Infinitesimal Formulation On ? -- Chapter 5. Relation to Hilbert-Brunn-Minkowski Operator and Linear Equivariance -- 5.1. Hilbert-Brunn-Minkowski operator -- 5.2. Linear equivariance of the Hilbert-Brunn-Minkowski operator -- 5.3. Spectral Minimization Problem and Potential Extremizers -- Chapter 6. Obtaining Estimates via the Reilly Formula -- 6.1. A sufficient condition for confirming the local -BM inequality -- 6.2. General Estimate on \D( ) -- 6.3. Examples -- Chapter 7. The second Steklov operator and \B( ??) -- 7.1. Second Steklov operator -- 7.2. Computing \B( ??) -- Chapter 8. Unconditional Convex Bodies and the Cube -- 8.1. Unconditional Convex Bodies -- 8.2. The Cube -- Chapter 9. Local log-Brunn-Minkowski via the Reilly Formula -- 9.1. Sufficient condition for verifying local log-Brunn-Minkowski -- 9.2. An alternative derivation via estimating \B( ) -- Chapter 10. Continuity of \B, \BNH, \D with application to _{ }? -- 10.1. Continuity of \B, \BNH, \D in -topology -- 10.2. The Cube -- 10.3. Unit-balls of ?_{ }? -- Chapter 11. Local Uniqueness for Even ^{ }-Minkowski Problem. 327 $aChapter 12. Stability Estimates for Brunn-Minkowski and Isoperimetric Inequalities -- 12.1. New stability estimates for origin-symmetric convex bodies with respect to variance -- 12.2. Improved stability estimates for all convex bodies with respect to asymmetry -- Bibliography -- Back Cover. 330 $a"The Lp-Brunn-Minkowski theory for p<1, proposed by Firey and developed by Lutwak in the 90's, replaces the Minkowski addition of convex sets by its Lp counterpart, in which the support functions are added in Lp-norm. Recently, Boroczky, Lutwak, Yang and Zhang have proposed to extend this theory further to encompass the range. In particular, they conjectured an Lp-Brunn-Minkowski inequality for origin-symmetric convex bodies in that range, which constitutes a strengthening of the classical Brunn-Minkowski inequality. Our main result confirms this conjecture locally for all (smooth) origin-symmetric convex bodies in Rn and. In addition, we confirm the local log-Brunn-Minkowski conjecture (the case ) for small-enough C2-perturbations of the unit-ball of for q 2, when the dimension n is sufficiently large, as well as for the cube, which we show is the conjectural extremal case. For unit-balls of with q, we confirm an analogous result for , a universal constant. It turns out that the local version of these conjectures is equivalent to a minimization problem for a spectral-gap parameter associated with a certain differential operator, introduced by Hilbert (under different normalization) in his proof of the Brunn- Minkowski inequality. As applications, we obtain local uniqueness results in the even Lp-Minkowski problem, as well as improved stability estimates in the Brunn- Minkowski and anisotropic isoperimetric inequalities"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 517 3 $aLocal 606 $aConvex domains 606 $aLp spaces 606 $aMinkowski geometry 606 $aInequalities (Mathematics) 606 $aConvex and discrete geometry -- General convexity -- Inequalities and extremum problems$2msc 606 $aConvex and discrete geometry -- General convexity -- Asymptotic theory of convex bodies$2msc 606 $aPartial differential equations -- Spectral theory and eigenvalue problems -- Estimation of eigenvalues, upper and lower bounds$2msc 606 $aGlobal analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Spectral problems; spectral geometry; scattering theory$2msc 615 0$aConvex domains. 615 0$aLp spaces. 615 0$aMinkowski geometry. 615 0$aInequalities (Mathematics) 615 7$aConvex and discrete geometry -- General convexity -- Inequalities and extremum problems. 615 7$aConvex and discrete geometry -- General convexity -- Asymptotic theory of convex bodies. 615 7$aPartial differential equations -- Spectral theory and eigenvalue problems -- Estimation of eigenvalues, upper and lower bounds. 615 7$aGlobal analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Spectral problems; spectral geometry; scattering theory. 676 $a516/.08 676 $a516.08 686 $a52A40$a52A23$a35P15$a58J50$2msc 700 $aKolesnikov$b Alexander V$01800464 701 $aMilman$b Emanuel$0739651 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910966324603321 996 $aLocal Lp-Brunn-Minkowski inequalities for p$94345288 997 $aUNINA