A5101513643- Plasma Applications and Diagnostics
- Relativity and Gravitational Theory
- Plasma and Flow Control in Aerodynamics
- Cosmology and Gravitation Theories
- Plasma Diagnostics and Applications
- Nonlinear Partial Differential Equations
- Geophysics and Gravity Measurements
- Combustion and flame dynamics
- Numerical methods in inverse problems
- Vacuum and Plasma Arcs
- Analytic and geometric function theory
- Geophysics and Sensor Technology
- Quantum Mechanics and Applications
- Combustion and Detonation Processes
- Advanced Mathematical Modeling in Engineering
- Black Holes and Theoretical Physics
- Spectral Theory in Mathematical Physics
- Fusion and Plasma Physics Studies
- Laser Design and Applications
- Pulsars and Gravitational Waves Research
- Earthquake Detection and Analysis
- Mathematical Dynamics and Fractals
- Flow Measurement and Analysis
- Material Science and Thermodynamics
- Holomorphic and Operator Theory
Lomonosov Moscow State University
2008-2025
Princeton University
2024
University of Geneva
2024
Institute for High Energy Physics
1996-2011
Moscow State University
2008-2009
$\def\Volume{\operatorname{Volume}}$ Let $(M^n, g)$ be a compact $n$-dimensional Riemannian manifold without boundary, where $g = (g_{ij})$ is $C^1$-smooth. Consider the sequence of eigenfunctions $u_k$ Laplace operator on $M$. $B$ ball We prove that number nodal domains intersect not greater than \[ C_1 \dfrac{\Volume_g (B)}{\Volume_g(M)} k + C_2 k^\frac{n-1}{n} \: , \] $C_1, C_2$ depend The problem local bounds for volume and was raised by Donnelly Fefferman, who also proposed an idea how...