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NODAL SET UPPER BOUND

For the real-analytic case, the Yau conjecture on nodel set Hausdorff measure was done by Donelly and Fefferman and there has been progress on the smooth case incrementally with the final step resolved by Logunov in 2016.  Logunov also has upper bounds by polynomial of the frequency.  So I am intrigued by the problem because it seems to me that the suggestion in Steinberger’s thesis of using the heat content is right.  Gilkey and many others have carefully worked out the heat content asymptotics p_t(x) \sim \sum a_n t^{n/2} for small times.  The basic idea is that the Yau conjecture bounds can be read off from the first term \int_N p_t(x) dx \sim c \cal{H}^{n-1}(\partial N) \sqrt{t} for small time which then gives the Yau conjecture bounds for t \sim \lambda^{1/2}.

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One of the problems with being the sole superpower, regardless of how strong the military is, without thoughtful farsighted leadership is this — everything America has done since the false flag of 9/11 including spinning a war on radical Islam and destroying a few countries in the Middle East — is that everyone except Americans knew clearly all along that the whole thing was political spin at home and funding of the military-industrial complex for these expensive wars abroad.  So China responds with Silk Road development project affecting 65 countries including Israel with the slow patient plan of bringing all these countries in China’s orbit, creating and managing the greatest industrialized area with cheapish labor and entire economies to revive to get growth to China’s 6-8 percent and essentially taking over the world without a shot fired.  It is very easy for China to talk about the dangers of radical Islam while not worrying much about the local politics at all because China is taking the far-sighted bet that these radical Islamists are not actually a big problem.  Julian Assange leaked documents in fact claiming that America and Israel had been holding up ISIS as pawns which makes sense so the whole thing is just a geostrategic security game that China can ignore while going for world supremacy economically and closing the gap with America militarily by 2049.  And now they are guaranteeing multilateral trade organizations as Trump threatens to shut them down.  This is pure unmitigated disaster for the world order that had kept world peace for 70 years since Bretton Woods.  China’s play is extremely farsighted and will succeed unless serious thinkers get at the helm of America which seems less and less likely.  This is no time for another game of big business taking over America.  Of course I can scream at the wind because Americans have bought into the Crusades doctrine and now Trump’s ultra-nationalists have declared their war on everyone who is not themselves.

Trump is not competing in world leadership at all — he’s playing schoolyard bully with Kim Jung Un.  America is better off not talking about nationalism at all. If the nation is healthy and strong talking about win-win cooperation with no feeling of superiority is a strong policy. Xi Jinping is a stable genius, Trump should learn something from a truly great world leader,  This is a serious handicap for America when China is expanding into industrialization of West Asia with the Silk Road project and the infrastructure development bank of Asia as a competitor to World Bank.  Whatever ’emotional intelligence’ Trump has in demagogy is no substitute for global vision and positive expansion and development that China is offering to the people of the world.  Chinese approach to global hegemony and the backer of globalized trade is reminiscent of the productivity of Bill Gates and Microsoft.  There is little doubt that Xi Jinping’s China is willing and capable of transforming the world order through peace and development.  America needs a comparable positive concrete vision for the world and leadership with comparable commitment to be the global hegemon.  Without deep historical understanding and a positive vision, Trump is simply accelerating the demise of the American world empire.

Chinese leadership today are the most cosmopolitan enlightened talented diplomatic and geopolitically visionary leadership for world order. Xi Jinping totally outclasses Donald Trump’s inward parochial and nationalistic vision for America which is a great shame because America needed its own Xi Jinping to reinforce and expand America’s engagement with the world. No great power with global interests can afford to produce ignorant hostile relations with the hundreds of countries with whom win-win non-imperial cooperation is necessary. Rhetoric matters. When Xi Jinping assures countries around the world for China’s democratic win-win cooperation for infrastructure building without short term profits, countries will listen and China will expand its influence across West Asia and Africa and essentially buy into the economic development of the entire planet which they will turn into the bloc that drives global growth with a deep finger in the benefits of that growth. America’s stance by contrast is hostile and recalcitrant and arrogant and unless there is a deep rethinking UNCOMPETITIVE in attracting cooperation. If America is seen as an imperious hostile power across the globe compared to China, the 70 years of American hegemony and influence will be cast aside as a hostile power that deprived the world of its deserved prosperity.

WORLD LOVER

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Fundamental physics has hit a snag after the coup by 1973 of the Standard Model which established itself as the frontier in July 4 2012 with the discovery of Higgs.  Without experimental evidence for string theory there are diverse approaches to a quantum theory of gravity.  My viewpoint has been since 2008 that in fact the problem is not quantising gravity as much as geometrising quantum.  This essentially means we are dealing with a big problem, and that is the wrongness of cosmology.  The evidence for dark matter and dark energy are extremely tenuous.  I have maintained that fundamental physics cannot be put together coherently until big bang cosmology is sliced up and reformed.  We are dealing with an eternal static universe by and large but it is not a flat universe.  Flat Minkowski space is an un-empirical idealization and parsimonious explanations are needed for the cosmic background radiation after Big Bang singularity is removed from reality.  Dark energy is explained without introduction of fictitious ‘energy’ without any experimental support by ambient curvature of the universe that could explain both quantisation of energy as well as the positive cosmological constant if Einstein’s gravitational field equations are interpreted simply as our physical universe being a hypersurface of a scaled four-sphere of fixed radius.  A re-examination of the evidence for dark matter could be explained in a curved universal geometry.  I believe these problems arise from a fundamentally wrong flat Minkowski space model of the cosmos.  We are dealing with GLOBAL problems of physics which need to explain quantum phenomena as consequences of global geometry.  This is the missing link of twentieth century physics for which superstring theory is an ambitious error that arises from attempting to globalize quantum field theory which is constructed from local phenomena.  The right question to ask is what is the geometric explanation of quantum phenomena.  The idea would be to go backward from a fundamental new geometric cosmology that accomodates the Standard Model rather than starting from quantum field theory on flat Minkowski space.  General relativity is too loose in specifying the equations of gravity and this is why there is confusion.  It should be interpreted as Ricci curvature of hypersurfaces of a fixed ambient spherical geometry.

Trump is wasting his time on trying to modify the Iran deal. NORMALIZING relations with Iran with the deal intact would have been the obvious good decision that he campaigned against. The reality is that this anti-Muslim crusades sparked by Israeli operation of 9/11 will have the long term effect of ensuring faster Chinese hegemony. Right now the real problem is not that American economy is doing poorly but RELATIVE problem that China and India are pushing the economic center of gravity eastward and the developing nations are carrying the brunt of global economic growth. The racists and xenophobic isolationism represented by Trump will only have the effect of putting America behind in the geopolitical scramble for growth and wealth. America has had limited success since 9/11 of producing a world order where America can dominate by threat of military force. This sort of hard power had never worked for global hegemony. Looking back, American hegemony was ensured because America had exported universal values and went against the narrow nationalisms of Europe and elsewhere. Europe, China and Russia are all much more vocal in their insistence of spreading of universal values and Trump went precisely backward. THEY have stolen America’s thunder as America’s moral high ground is being lost and thus GUTTED America cannot retain dominance or hegemony by military might alone. America would not have won the Second World War — although Russia really won the ground war with 20 million lives — without a universalist outlook.

 

People who believe that they understand the gritty side of how the world works and are cynical because they see that most people are unprincipled with mean interests and who are fundamentally corrupt underestimate the fact that it is extraordinary people with high ideals and grand visions and deep characters who transform and influence the world and that most of the cynical people who look at the mean and low side of human character are in the bottom of the barrel by and large with some able to amass wealth by sculduggery. In America, the collapse of high ideals and meanness as a way of life represented by Trump’s ascension is a sign of rot and decay and the only hope for America remains in a change of American consciousness so that America once again DESERVES to be the hegemonic power. This is no silly idealism. America is risking its life and future prosperity by having a bad applie like Trump influencing the public outlook. Trump is a deeply corrupt and rotten character, and just like any rotten character he is degrading American national psyche by being the President. American economy will work fine but the ENERGY of the country is being mishandled badly because of his rotten character. The hope is that better people than Trump in America will react by embarrassment enough to take this nation higher. Every year that Trump is the role model of America, there will be a degeneration of America’s global influence.

South Korea is essentially an American colony since the Korean war.  I think Trump administration’s policy toward North Korea is allowing North-South talks to proceed without American involvement and essentially the American attack plans on North Korea will backfire and Korean unification process will begin with quiet influence of China in the back.  This can be avoided, but I don’t think Trump’s people have the competence or the mindset to do much but rush the ‘South Korean independence’ from America.