The lackluster performance in China and Japan, along with alarmingly weak export data from South Korea and Taiwan, put the burden of supporting global growth squarely on Europe and particularly the United States, which is struggling to get back on track after a fierce winter. China’s factory activity contracted for the third straight month in May as domestic and export orders shrank, a private survey showed, adding to views that Beijing will have to roll out its most aggressive stimulus measures since the global financial crisis to avert a sharper slowdown.