We construct a quasi-Banach space which cannot be given an equivalent plurisubharmonic quasi-norm, but such that it has a quotient by a onedimensional space which is a Banach space. We then use this example to construct a compact convex set in a quasi-Banach space which cannot be atfinely embedded into the space L0 of all measurable functions.

Donaldson conjectured[14] that the space of Kähler metrics is geodesic convex by smooth geodesic and that it is a metric space. Following Donaldson’s program, we verify the second part of Donaldson’s conjecture completely and verify his first part partially. We also prove that the constant scalar curvature metric is unique in each Kähler class if the first Chern class is either strictly negativ...

We prove existence and uniqueness of the gradient flow of the Entropy functional under the only assumption that the functional is λ-geodesically convex for some λ ∈ R. Also, we prove a general stability result for gradient flows of geodesically convex functionals which Γ−converge to some limit functional. The stability result applies directly to the case of the Entropy functionals on compact sp...

We establish extremal values of a solution y of a second-order initial value problem as the coefficients vary in a nonconvex set. These results extend earlier work by M. Essen in particular by allowing a coefficient in the second derivative expression.

Let (Ω,Σ) be a measurable space, with Σ a sigma-algebra of subset of Ω, and let C be a nonempty bounded closed convex separable subset of a Banach space X , whose characteristic of noncompact convexity is less than 1, KC(X) the family of all compact convex subsets of X . We prove that a multivalued nonexpansive non-self-random operator T :Ω×C → KC(X), 1-χ-contractive mapping, satisfying an inwa...

In this paper, we prove that the distance function of an open connected set in R with a C boundary is superharmonic in the distribution sense if and only if the boundary is weakly mean convex. We then prove that Hardy inequalities with a sharp constant hold on weakly mean convex C domains. Moreover, we show that the weakly mean convexity condition cannot be weakened. We also prove various impro...

In this paper we show that the waiting and the sojourn times of a customer in a single-stage, multiple-server, G / G /c queueing system are increasing and starshaped with respect to the mean service time. Usefulness of this result in the design of the optimal service speed in the G / G /c queueing system is also demonstrated. SECOND-ORDER PROPERTIES; SINGLE-STAGE QUEUEING SYSTEMS; STOCHASTIC ST...

A convexity structure satisfies the separation property 5'4 if any two disjoint convex sets extend to complementary half-spaces. This property is investigated for alignment spaces, n-ary convexities, and graphs. In particular, it is proven that a) an n-ary convexity is $4 iff every pair of disjoint polytopes with at most n vertices can be separated by complementary half spaces, and b) an interv...

We give a complete characterization of those f : [0, 1]→ X (where X is a Banach space) which allow an equivalent (smooth) parametrization with finite convexity, and (in the case when X has a Fréchet smooth norm) a C parametrization. For X = R, a characterization for the C case is well-known. However, even in the case X = R, several quite new ideas are needed.

We prove that a Banach space X has normal structure provided it contains a finite codimensional subspace Y such that all spreading models for Y have normal structure. We show that a Banach space X is strictly convex if the set of fixed points of any nonexpansive map defined in any convex subset C C X is convex and give a sufficient condition for uniform convexity of a space in terms of nonexpan...