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1 | (8) |
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1.1 Previously Known Partial Results |
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2 | (1) |
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3 | (2) |
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1.3 Spectral Interpretation via the Hilbert--Brunn--Minkowski operator |
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5 | (1) |
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6 | (1) |
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6 | (3) |
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9 | (2) |
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Chapter 3 Global vs. Local Formulations of the Lp-Brunn--Minkowski Conjecture |
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11 | (6) |
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3.1 Standard Equivalent Global Formulations |
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11 | (1) |
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3.2 Global vs. Local Lp-Brunn--Minkowski |
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12 | (5) |
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Chapter 4 Local Lp-Brunn--Minkowski Conjecture -- Infinitesimal Formulation |
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17 | (8) |
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4.1 Mixed Surface Area and Volume of C2 functions |
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17 | (1) |
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4.2 Properties of Mixed Surface Area and Volume |
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18 | (2) |
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4.3 Second Lp-Minkowski Inequality |
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20 | (1) |
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4.4 Comparison with classical p = 1 case |
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21 | (1) |
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4.5 Infinitesimal Formulation On Sn-1 |
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21 | (1) |
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4.6 Infinitesimal Formulation On ∂K |
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22 | (3) |
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Chapter 5 Relation to Hilbert--Brunn--Minkowski Operator and Linear Equivariance |
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25 | (12) |
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5.1 Hilbert--Brunn--Minkowski operator |
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26 | (4) |
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5.2 Linear equivariance of the Hilbert--Brunn--Minkowski operator |
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30 | (3) |
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5.3 Spectral Minimization Problem and Potential Extremizers |
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33 | (4) |
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Chapter 6 Obtaining Estimates via the Reilly Formula |
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37 | (8) |
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6.1 A sufficient condition for confirming the local p-BM inequality |
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38 | (2) |
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6.2 General Estimate on D(K) |
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40 | (1) |
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41 | (4) |
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Chapter 7 The second Steklov operator and BH(Bn2) |
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45 | (4) |
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7.1 Second Steklov operator |
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45 | (1) |
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46 | (3) |
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Chapter 8 Unconditional Convex Bodies and the Cube |
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49 | (4) |
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8.1 Unconditional Convex Bodies |
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49 | (1) |
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50 | (3) |
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Chapter 9 Local log-Brunn--Minkowski via the Reilly Formula |
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53 | (4) |
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9.1 Sufficient condition for verifying local log-Brunn--Minkowski |
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53 | (2) |
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9.2 An alternative derivation via estimating Bh(K) |
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55 | (2) |
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Chapter 10 Continuity of BH, B, D with application to Bnq |
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57 | (4) |
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10.1 Continuity of BH, B, D in C-topology |
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57 | (1) |
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58 | (2) |
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60 | (1) |
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Chapter 11 Local Uniqueness for Even Lp-Minkowski Problem |
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61 | (4) |
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Chapter 12 Stability Estimates for Brunn--Minkowski and Isoperimetric Inequalities |
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65 | (10) |
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12.1 New stability estimates for origin-symmetric convex bodies with respect to variance |
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65 | (5) |
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12.2 Improved stability estimates for all convex bodies with respect to asymmetry |
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70 | (5) |
| Bibliography |
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