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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.
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 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.
Physicists have developed a new optical centrifuge that can precisely spin molecules inside a superfluid for the first time。 The advance could help unravel some of the biggest mysteries of quantum liquids and reveal how superfluidity breaks down at the atomic scale
A strange "chirping" signal from a distant supernova has revealed the birth of a magnetar, confirming that these incredibly magnetic neutron stars can power the universe's brightest stellar explosions。 The discovery also marks the first time Einstein's general relativity has been used to explain the mechanics of a supernova
Water’s odd behavior becomes even more dramatic when it is supercooled, but scientists have struggled to compare the many different ways of describing its microscopic structure。 Researchers at the University of Osaka used an AI model trained on computer simulations to evaluate 16 different structural descriptors。 The system identified the most effe
Preclinical trial is testing the feasibility of humanoid robots in surgery
Engineers at a deep underground research facility noticed something strange during major rainstorms: airflow underground sometimes reversed direction。 Using new sensors and mathematical modeling, they found that water rushing down a shaft was effectively pushing air through the tunnels like a giant piston。 The breakthrough explains a long-standing
Two newly confirmed "super-puff" planets are so diffuse that they are less dense than cotton candy, despite being about the size of Jupiter。 Their rare orbital relationship and enormous, lightweight atmospheres could provide valuable clues about how some of the strangest planets in the galaxy come to exist
A centimeter-sized crystal has revealed clear signs of quantum entanglement, showing that large, everyday objects can display surprisingly deep quantum behavior。 The discovery could help solve the mystery of strange metals while opening new possibilities for ultra-precise quantum sensors and other advanced technologies
Scientists have rewritten the story of gallium after discovering that its unusual atomic bonds re-form at high temperatures, contradicting decades of accepted theory。 The finding changes how researchers explain why the metal melts so easily and behaves unlike almost any other metal。 Beyond solving a long-standing scientific mystery, the work could
Scientists have combined machine learning with quantum physics to discover two new superconductors and create a much faster way to search for many more。 The technique could bring researchers significantly closer to the long-sought goal of a room-temperature superconductor
A new sunlight-powered material can convert visible light into higher-energy UV light, overcoming a challenge that has frustrated scientists for years。 The breakthrough could enable cleaner air purification, solar-driven chemistry, and advanced manufacturing technologies using nothing more than natural sunlight
Hubble has captured a spectacular view of LH 95, where about 2,500 young stars are still on their journey to becoming full-fledged stars。 Scientists discovered these growing stars can keep pulling in gas and dust for millions of years, extending an important stage of stellar development。 The region also contains multiple generations of stars living
Researchers have created quantum control techniques that can make a system appear to run backward in time。 By precisely managing quantum measurements, they can reshape the system's arrow of time and even harvest energy from the measurement process itself。 The breakthrough could lead to more powerful quantum computers, quantum batteries, and other a