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Essential normality for quotient modules and complex dimensions
On Aleksandrov-Fenchel Inequalities for k-Convex Domains
In this lecture notes, we will discuss the classical Aleksandrov-Fenchel inequalities for quermassintegrals on convex domains and pose the problem of how to extend the inequalities to non-convex
A subelliptic Bourgain-Brezis inequality
We prove an approximation lemma on (stratified) homogeneous groups that allows one to approximate a function in the non-isotropic Sobolev space $\dot{NL}^{1,Q}$ by $L^{\infty}$ functions,
Isoperimetric inequality on CR-manifolds with nonnegative $Q'$-curvature
In this paper, we study contact forms on the three- dimensional Heisenberg manifold with its standard CR structure. We discover that the $Q'$-curvature, introduced by Branson, Fontana and Morpurgo
Some higher order isoperimetric inequalities via the method of optimal transport
In this paper, we establish some sharp inequalities between the volume and the integral of the $k$-th mean curvature for $k+1$-convex domains in the Euclidean space. The results generalize the
Nonuniqueness for a fully nonlinear boundary Yamabe-type problem via bifurcation theory
AbstractOne way to generalize the boundary Yamabe problem posed by Escobar is to ask if a given metric on a compact manifold with boundary can be conformally deformed to have vanishing $$\sigma
Semiflows "Monotone with Respect to High-Rank Cones" on a Banach Space
It is shown that for a pseudoordered precompact semiorbit the $omega$-limit set $\omega(x)$ either is ordered, or is contained in the set of equilibria, or possesses a certain ordered homoclinic property.
Geometric Arveson-Douglas Conjecture and Holomorphic Extension
In this paper we introduce techniques from complex harmonic analysis to prove a weaker version of the Geometric Arveson-Douglas Conjecture for complex analytic subsets that is smooth on the boundary