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51. The linear trace Harnack quadratic on a steady gradient Ricci soliton satisfies the heat equation

52. A necessary and sufficient condition for Ricci shrinkers to have positive AVR

53. Convex functions on Riemannian manifolds

54. Heat kernel for evolving metrics

56. Elementary aspects of metric geometry

59. Perelman’s pseudolocality theorem

60. Heat kernel for static metrics

62. Entropy, 𝜇-invariant, and finite time singularities

63. Compactness of the space of 𝜅-solutions

72. Local derivative of curvature estimates

74. Closed manifolds with positive curvature

75. Differential Harnack estimates of LYH-type

77. Perelman’s differential Harnack estimate

79. The compactness theorem for Ricci flow

81. Proof of the compactness theorem

82. Ricci solitons

83. Entropy and no local collapsing

84. Energy, monotonicity, and breathers

85. Basic topology of 3-manifolds

86. The reduced distance

90. Riemannian geometry

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