搜索结果：Geometriae dedicata

Relatively little is known about the discrete horospheres in hyperbolic groups, even in simple settings. In this paper we work with hyperbolic one-ended right-angled Coxeter groups and describe two graph structures that mimic the intrinsic metric on a classical horosphere: the Rips graph and the divergence graph (the latter due to Cohen, Goodman-Strauss, and Rieck). We develop, analyze, and implement algorithms based on finite-state machines that draw large finite portions of these graphs, and deduce various geometric corollaries about the path metrics induced by these graph structures.

Let $G$ be a compact Lie group. We study a class of Hamiltonian $(G \times S^{1})$-manifolds decorated with a function $s$ with certain equivariance properties, under conditions on the $G$-action which we call of (semi-)linear type. In this context, a close analogue of hyperkähler reduction is defined, and our main result establishes surjectivity of an appropriate analogue of Kirwan's map. As a particular case, our setting includes a class of hyperkähler manifolds with trihamiltonian torus actions, to which our surjectivity result applies.

We construct complete Calabi-Yau metrics on non-compact manifolds that are smoothings of an initial complete intersection $V_0$ that is a Calabi-Yau cone, extending the work of Székelyhidi (2019). The constructed Calabi-Yau manifold has tangent cone at infinity given by $\mathbb{C} \times V_0$. This construction produces Calabi-Yau metrics with fibers having varying complex structures and possibly isolated singularities.

These notes are a companion to the article "Lorentz spacetimes of constant curvature" by Geoffrey Mess, which was first written in 1990 but never published. Mess' paper will appear together with these notes in a forthcoming issue of Geometriae Dedicata.

Median spaces are spaces in which for every three points the three intervals between them intersect at a single point. It is well known that rank-1 affine buildings are median spaces, but by a result of Haettel, higher rank buildings are not even coarse median. We define the notion of ``2-median space'', which roughly says that for every four points the minimal discs filling the four geodesic triangles they span intersect in a point or a geodesic segment. We show that CAT(0) Euclidean polygonal complexes, and in particular rank-2 affine buildings, are 2-median. In the appendix, we recover a special case of a result of Stadler of a Fary-Milnor type theorem and show in elementary tools that a minimal disc filling a geodesic triangle is injective.

We determine the Néron-Severi lattices of $K3$ hypersurfaces with large Picard number in toric three-folds derived from Fano polytopes. On each $K3$ surface, we introduce a particular elliptic fibration. In the proof of the main theorem, we show that the Néron-Severi lattice of each $K3$ surface is generated by a general fibre, sections and appropriately selected components of the singular fibres of our elliptic fibration. Our argument gives a certain proof of the Dolgachev conjecture for Fano polytopes, which is a conjecture on mirror symmetry for $K3$ surfaces.

Scientists have identified new clues that could help astronomers spot one of the most famous hypothetical alien megastructures: a Dyson sphere。 The study finds that red dwarfs and white dwarfs are the most promising stars to examine, since advanced civilizations could potentially build energy-harvesting swarms around them more easily。 These objects

A new quantum theory bridges two rival models of how impurities behave inside many-particle systems, resolving a problem that has challenged physicists for decades。 The findings could reshape experiments on ultracold atoms, semiconductors, and other exotic forms of quantum matter

Astronomers may have witnessed one of the rarest and most dramatic cosmic events ever seen: a long-sought intermediate-mass black hole ripping apart a dense white dwarf star and devouring it。 The Einstein Probe space telescope caught the explosion in its earliest moments, revealing an unusual sequence of intense X-ray flashes unlike anything seen i

A new quantum device can generate precisely controlled bursts of sound-like particles, or phonons, by forcing electrons through an ultra-thin crystal at extremely low temperatures。 The surprising behavior pushes beyond the limits predicted by current theories, suggesting scientists need to rethink how energy moves through advanced materials。 In the

Researchers have proposed that black holes stop evaporating at the last moment, leaving behind tiny remnants that preserve all the information they contain。 The same seven-dimensional geometry behind this idea could also help explain why elementary particles have mass

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A decades-old puzzle about water has finally been unraveled。 Researchers found that water trapped in tiny nanoscale spaces is not inherently more reactive。 Instead, the intense pressures created inside these microscopic gaps explain most of the effect, while the surrounding material can further enhance water's chemistry if it interacts with the rea

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Ancient asteroid impacts may have done more than reshape Earth's surface—they could have helped spark life itself。 New computer models show the collisions created enormous underground hydrothermal systems by cracking the planet's crust and allowing hot water to flow through it。 These long-lasting, life-friendly environments may have covered much of

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