Tootfinder

Scalar-mean rigidity theorem and Llarull's theorem for nonspin manifolds
Gaoming Wang, Jinmin Wang, Zhizhang Xie, Bo Zhu
https://arxiv.org/abs/2609.15907 https://arxiv.org/pdf/2609.15907 https://arxiv.org/html/2609.15907
arXiv:2609.15907v1 Announce Type: new
Abstract: We prove Llarull's scalar curvature rigidity theorem for spheres and scalar-mean rigidity for strictly convex Euclidean domains in all dimensions without the spin assumption.
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І ці люди забороняють нам колупатися в носі.
АМОГУС.
tl;dr Люди на спектрі більш схильні дотримуватися законів, ніж нейротіпікали, у випадку, коли за ними ніхто не спостерігає.
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tl;dr People on the spectrum tend to follow the laws more reliably when not watched (than the neurotypicals in the same conditions).
The paper calls it "moral rigidity".
I'm not sure if "flexibility" in this case is something to be proud of. What do you think?…

Rigid Functions, IP-Systems, and Topological Mild Mixing
Song Shao, Hui Xu
https://arxiv.org/abs/2608.02282 https://arxiv.org/pdf/2608.02282 https://arxiv.org/html/2608.02282
arXiv:2608.02282v1 Announce Type: new
Abstract: We study uniform rigidity and topological mild mixing through continuous observables. For a fixed sequence of times, the observables rigid along that sequence form a closed unital $T^{\pm1}$-invariant algebra and determine the maximal factor uniformly rigid along the prescribed sequence. We then give functional forms of the classical ${\rm SIP}^{*}$- and ${\rm IP}^{*}$-return-time criteria: a topological dynamical system is mildly mixing exactly when it has no nonconstant locally SIP-rigid observable, and in the minimal category the same property is equivalent to the absence of nonconstant locally IP-rigid observables. Finally, a locally IP-rigid observable yields a canonical orbit-name factor carrying marked local data. For fixed local data, the $T^{\pm 1}$-invariant core of the local rigidity algebra determines a uniformly rigid factor whenever the core is nontrivial.
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Stability of Einstein 4-manifolds satisfying a chiral curvature condition
Diego Artacho
https://arxiv.org/abs/2609.15159 https://arxiv.org/pdf/2609.15159 https://arxiv.org/html/2609.15159
arXiv:2609.15159v1 Announce Type: new
Abstract: Let $(M,g)$ be a compact oriented Einstein four-manifold with Einstein constant $E$ and let $\widehat{R}^ $ denote the action of the Riemann curvature tensor on self-dual two-forms. We show that if $\widehat{R}^ < 0$, then $g$ is strictly linearly stable for the Einstein-Hilbert functional, thus giving a chiral criterion for stability. Our result is stronger than the one by Fine-Krasnov-Singer, who conclude local rigidity from $\widehat{R}^ < 0$ by proving stability for a different action functional. Our proof proceeds by showing that $(M,g)$ admits a natural spin$^h$ structure carrying a non-zero parallel spin$^h$-spinor. We then apply a lower bound on the Lichnerowicz Laplacian on traceless symmetric two-tensors in the presence of such a spinor.
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"Germany unveils strategy for becoming Europe’s strongest military by 2039" did they mean Germany über alles? 😳
Is it a sequel or third in a trilogy?
https://www.defensenews.com/global/europe/202…

Germany unveils strategy for becoming Europe’s strongest military by 2039
The Bundeswehr will move away from rigid hardware quotas − the number of tanks, aircraft or ships − toward a flexible, effects-based planning model.

Replaced article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/3]:
- Family index for Fredholm extensions of semi-Fredholm operators
Marina Prokhorova
https://arxiv.org/abs/2401.16060 https://mastoxiv.page/@arXiv_mathDG_bot/111843359116350796
- Constructing stable Hilbert bundles via Diophantine approximation
Yucheng Liu, Biao Ma
https://arxiv.org/abs/2501.15784
- Ricci Solitons of Left-Invariant Metrics on Lie Groups with Derived Algebra of Dimension at Most Two
Hamid Reza Salimi Moghaddam
https://arxiv.org/abs/2601.10730 https://mastoxiv.page/@arXiv_mathDG_bot/115920688396400257
- Mass and rigidity in almost K\"ahler geometry
Partha Ghosh
https://arxiv.org/abs/2603.08627 https://mastoxiv.page/@arXiv_mathDG_bot/116204063956883755
- Classifying Slice-Regular Polynomials via Group Actions on the Twistor Space
Chunlin Liu, Giovanni Moreno, Haipan Shi
https://arxiv.org/abs/2605.22788 https://mastoxiv.page/@arXiv_mathDG_bot/116617182455085202
- $G_2$ and the Maximally Symmetric (3, 8) Distribution with 6-Dimensional Square
Nicklas Day, Boris Doubrov, Igor Zelenko
https://arxiv.org/abs/2605.25910 https://mastoxiv.page/@arXiv_mathDG_bot/116639966776117301
- Cohn--Vossen-Type Inequalities for Three-Manifolds and Locally Conformally Flat Manifolds
Jialong Deng
https://arxiv.org/abs/2606.01368 https://mastoxiv.page/@arXiv_mathDG_bot/116679534951132380
- From Gradient Descent to Potential Theory: A Geometric Dictionary for Binary Classification
Catalin Vasii
https://arxiv.org/abs/2607.00988 https://mastoxiv.page/@arXiv_mathDG_bot/116849328935224137
- A sharp relative comparison inequality for conformal fillings of Poincar\'e--Einstein manifolds
Nan Wu
https://arxiv.org/abs/2607.13742 https://mastoxiv.page/@arXiv_mathDG_bot/116928601640640156
- A degenerate free boundary minimal annulus and non-uniqueness in spherical caps beyond the hemisp...
Alexander Pigazzini
https://arxiv.org/abs/2607.23534 https://mastoxiv.page/@arXiv_mathDG_bot/116996542129550830
- Special Lagrangians with multiple isolated singularities
Bryan Dimler, Filippo Gaia
https://arxiv.org/abs/2607.26302 https://mastoxiv.page/@arXiv_mathDG_bot/117007805427278588
- Demailly-Koll\'ar continuity on klt pairs, and applications to alpha and delta invariants
Tam\'as Darvas, Kewei Zhang
https://arxiv.org/abs/2608.23505 https://mastoxiv.page/@arXiv_mathDG_bot/117155289132945927
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Degrees of Maps and Cohomological Rigidity of Partial Flag Manifolds
Manas Mandal
https://arxiv.org/abs/2608.09183 https://arxiv.org/pdf/2608.09183 https://arxiv.org/html/2608.09183
arXiv:2608.09183v1 Announce Type: new
Abstract: We study the existence of continuous maps with nonzero Brouwer degree between partial flag manifolds. We prove that every continuous map between two distinct complex (or, quaternionic) partial flag manifolds, whose codomain is not a Grassmannian, has Brouwer degree zero. This establishes, for such partial flag manifolds, the analogue of the results of Ramani-Sankaran and Sankaran-Sarkar for complex and quaternionic Grassmannians, as well as an algebraic-geometric result of Paranjape and Srinivas for complex Grassmannians. As a consequence, we prove that complex and quaternionic partial flag manifolds are cohomologically rigid; that is, their rational cohomology rings determine their homeomorphism types. We conjecture that complex and quaternionic partial flag manifolds are homologically rigid.
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Yes, both are called "floppy disk", the "floppy" refers to the disk inside the shell (a flexible plastic disk coated with a magnetic storage medium).
Just as "hard disk" refers to the rigid coated disks inside the case of a hard disk drive.

The reason:
The brain gives possible losses more weight than possible benefits. A past failure can make a new choice feel unsafe after the facts change. Limited time, unclear authority, slow approval, rigid processes, and weak support can also block growth.

Dihedral Rigidity for Convex Polytopes by Smooth Approximation
Yuchen Bi
https://arxiv.org/abs/2608.06320 https://arxiv.org/pdf/2608.06320 https://arxiv.org/html/2608.06320
arXiv:2608.06320v1 Announce Type: new
Abstract: Following Brendle's smooth approximation approach, we give a proof of Gromov's dihedral rigidity conjecture for convex polytopes.
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