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result(s) for
"Hyperspace."
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Elliptic Virtual Structure Constants and Gromov-Witten Invariants for Complete Intersections in Weighted Projective Space
In this paper, we generalize our formalism of the elliptic virtual structure constants to hypersurfaces and complete intersections within certain weighted projective spaces possessing a single Kähler class.
Journal Article
Black holes in higher dimensions
\"Black holes are one of the most remarkable predictions of Einstein's general relativity. Now widely accepted by the scientific community, most work has focussed on black holes in our familiar four spacetime dimensions. But in recent years, ideas in brane-world cosmology, string theory, and gauge/gravity duality have all motivated a study of black holes in more than four dimensions, with surprising results. In higher dimensions, black holes exist with exotic shapes and unusual dynamics. Edited by leading expert Gary Horowitz, this exciting book is the first devoted to this new field. The major discoveries are explained by the people who made them: RobMyers describes theMyers-Perry solutions that represent rotating black holes in higher dimensions; Ruth Gregory describes the Gregory-Laflamme instability of black strings; and Juan Maldacena introduces gauge/gravity duality, the remarkable correspondence that relates a gravitational theory to nongravitational physics. There are two additional chapters on this duality describing how black holes can be used to describe relativistic fluids and aspects of condensed matter physics\"-- Provided by publisher.
Book
Nonexistence of non-Hopf Ricci-semisymmetric real hypersurfaces in and
In this paper, we solved an open problem raised by Cecil and Ryan (2015, Geometry of Hypersurfaces , Springer Monographs in Mathematics, Springer, New York, p. 531) by proving the nonexistence of non-Hopf Ricci-semisymmetric real hypersurfaces in$\\mathbb {C}P^{2}$and$\\mathbb {C}H^{2}$.
Journal Article
Generalized -Einstein Real Hypersurfaces in and
In this paper we obtain some new characterizations of pseudo-Einstein real hypersurfaces in$\\mathbb{C}P^{2}$and$\\mathbb{C}H^{2}$. More precisely, we prove that a real hypersurface in$\\mathbb{C}P^{2}$or$\\mathbb{C}H^{2}$with constant mean curvature is generalized${\\mathcal{D}}$-Einstein with constant coefficient if and only if it is pseudo-Einstein. We prove that a real hypersurface in$\\mathbb{C}P^{2}$with constant scalar curvature is generalized${\\mathcal{D}}$-Einstein with constant coefficient if and only if it is pseudo-Einstein.
Journal Article
Existence of infinitely many minimal hypersurfaces in positive Ricci curvature
In the early 1980s, S. T. Yau conjectured that any compact Riemannian three-manifold admits an infinite number of closed immersed minimal surfaces. We use min–max theory for the area functional to prove this conjecture in the positive Ricci curvature setting. More precisely, we show that every compact Riemannian manifold with positive Ricci curvature and dimension at most seven contains infinitely many smooth, closed, embedded minimal hypersurfaces. In the last section we mention some open problems related with the geometry of these minimal hypersurfaces.
Journal Article
The Kreuzer-Skarke axiverse
A
bstract
We study the topological properties of Calabi-Yau threefold hypersurfaces at large
h
1
,
1
. We obtain two million threefolds
X
by triangulating polytopes from the Kreuzer-Skarke list, including all polytopes with 240 ≤
h
1
,
1
≤ 491. We show that the Kähler cone of
X
is very narrow at large
h
1
,
1
, and as a consequence, control of the
α′
expansion in string compactifications on
X
is correlated with the presence of ultralight axions. If every effective curve has volume ≥ 1 in string units, then the typical volumes of irreducible effective curves and divisors, and of
X
itself, scale as (
h
1
,
1
)
p
, with 3 ≲
p
≲ 7 depending on the type of cycle in question. Instantons from branes wrapping these cycles are thus highly suppressed.
Journal Article
Factorizing random sets and type III Arveson systems
We develop a representative-level framework for the Liebscher-Tsirelson random-set construction of Arveson systems from stationary factorizing measure types. We introduce the notion of a measurable factorizing family of probability measures on hyperspaces of closed subsets of time intervals and prove that every such family canonically generates an Arveson system. Within this framework we obtain a purely measure-theoretic characterization of spatiality: positive normalized units correspond exactly to dominated families of measures that factorize strictly. We then present a general mechanism for constructing type III Arveson systems via infinite products of measurable factorizing families. Starting from a type II\\(_0\\) seed satisfying a quantitative Hellinger-smallness condition, we form a marked infinite product indexed by \\([0,1]\\times\\mathbb N\\) and show, using Kakutani's criterion, that the resulting product system admits no units. This yields a robust construction principle for type III random-set systems. As an application we analyze zero sets of Brownian motion. After anchor-adapted localization and Palm-type uniformization, the Brownian seed satisfies the required overlap estimates, and the associated infinite-product construction produces explicit examples of type III random-set systems, as anticipated in the work of Tsirelson and Liebscher.
Paper