Equivalence of Dimension-Free Harnack Inequality and Curvature Condition

52 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Gradient estimates for heat kernels and harmonic functions (2017, background): “(BE) |∇Ht f (x)|(2) ≤ Ht(|∇ f |(2))(x), which, on manifolds, is known to be equivalent to non-negativity of Ricci curvature; see [10] and also [8, 9, 111].”
Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below (2006, background): “On the other hand, since the formulation of the inequality in [26] is equivalent to an underlying lower curvature bound (see [31]), the formulation of the resulting inequality will be slightly different in the present paper.”
Noncommutative martingale deviation and Poincaré type inequalities with applications (2012, unknown): “[63]) 2( f, f ) ≥ α ( f, f ), f ∈ C∞(M).”
Equivalent semigroup properties for the curvature-dimension condition (2010, unknown): “[2, 10, 15, 19, 22] and references within for details.”
Harnack inequalities on manifolds with boundary and applications (2009, background): “[1, 3] for equivalent gradient and Poincaré/logSobolev inequalities, [11] for equivalent cost (or Wasserstein distance) inequalities, and [14] for equivalent dimension-free Harnack inequalities.”