NEAR OPTIMAL BOUNDS IN FREIMAN'S THEOREM

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<strong>IN</strong>HOMOGENEOUS QUADRATIC FORMS 137 Furthermore, if L is a null subspace (of the first type), then k ∈ K : d(atkL) 0 be small, and let A L,1 t (δ, ε) = k ∈ K : δ1+ε
138 MARGULIS and MOHAMMADI For simplicity, let ζ = qξ, where q ∈ SL4(R) was chosen such that Q(v) = B(qv) for all v ∈ R 4 . Fix t > 0 and 0
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NEAR OPTIMAL BOUNDS IN FREIMAN’S
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SUR LA NON-DENSITÉ DES POINTS ENTI
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30 CASIM ABBAS Recall that the Reeb
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32 CASIM ABBAS that Here the energy
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34 CASIM ABBAS • uτ ( ˙S) ∩ u
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36 CASIM ABBAS punctured surfaces w
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38 CASIM ABBAS that is, the central
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40 CASIM ABBAS even have A(r) ≡ 0
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42 CASIM ABBAS are contact forms on
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44 CASIM ABBAS the standard complex
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46 CASIM ABBAS and Jδε2 = xγ1(r)
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48 CASIM ABBAS (λ0,J0) with vanish
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50 CASIM ABBAS defined as H 1 j (S)
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52 CASIM ABBAS and denoting the cor
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54 CASIM ABBAS formula (2.2) for th
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56 CASIM ABBAS Restricting any of t
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58 CASIM ABBAS where fτ (∞) = li
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60 CASIM ABBAS for τ
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62 CASIM ABBAS Recalling our origin
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64 CASIM ABBAS THEOREM 3.7 Let µ,
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66 CASIM ABBAS Since w2 − w1C 1,
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68 CASIM ABBAS be the conformal tra
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70 CASIM ABBAS so that, for z ∈ B
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72 CASIM ABBAS and, for every R>0,
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74 CASIM ABBAS W 1,p loc (C) since
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76 CASIM ABBAS (follows from 0 =
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78 CASIM ABBAS is finite, the image
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80 CASIM ABBAS Converting from coor
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82 CASIM ABBAS [27] D. MCDUFF and D
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84 GUILLARMOU and TZOU where ∂ν
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Page 93 and 94: 94 GUILLARMOU and TZOU At a point (
Page 95 and 96: 96 GUILLARMOU and TZOU enough, we h
Page 97 and 98: 98 GUILLARMOU and TZOU Using the fa
Page 99 and 100: 100 GUILLARMOU and TZOU certain exp
Page 101 and 102: 102 GUILLARMOU and TZOU −1 where
Page 103 and 104: 104 GUILLARMOU and TZOU factor, or
Page 105 and 106: 106 GUILLARMOU and TZOU Proof of Pr
Page 107 and 108: 108 GUILLARMOU and TZOU where I1 =
Page 109 and 110: 110 GUILLARMOU and TZOU Proof of Le
Page 111 and 112: 112 GUILLARMOU and TZOU COROLLARY 6
Page 113 and 114: 114 GUILLARMOU and TZOU in x−k−
Page 115 and 116: 116 GUILLARMOU and TZOU Therefore,
Page 117 and 118: 118 GUILLARMOU and TZOU Proof of Pr
Page 119 and 120: 120 GUILLARMOU and TZOU [27] R. B.
Page 121 and 122: 122 MARGULIS and MOHAMMADI multiple
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Page 129 and 130: 130 MARGULIS and MOHAMMADI We fix s
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Page 133 and 134: 134 MARGULIS and MOHAMMADI Hence th
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NEAR OPTIMAL BOUNDS IN FREIMAN'S THEOREM

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